List of Publications of  Iskander A.  Taimanov

Articles recently published in

  • On the formality of nearly Kahler manifolds and of Joyce's examples in G_2-holonomy.
    arXiv:2012.10915 (with M. Amann)
  • Rectangular knot diagrams classification with deep learning.
    arXiv:2011.03498 (with L. Kauffman and N.E. Russkikh)
  • The second closed geodesic, the fundamental group, and generic Finsler metrics.
    arXiv:2011.01909 (with H.-B. Rademacher)
  • Representative elementary volume via averaged scalar Minkowski functionals.
    arXiv:2008.03727 (with M.V. Andreeva, A.V. Kalyuzhnyuk, V.V. Krutko, N.E. Russkikh)
  • Closed geodesics on connected sums and 3-manifolds.
    arXiv:1809.04588 (with H.-B. Rademacher)


  1. Modern Geometric Structures and Fields , Graduate Studies in Math., V. 71, AMS, 2006. 633 pp. (with S.P. Novikov)
    • Original Russian edition: Moscow: MCCME, 2005. 584 pp. (with S.P. Novikov) (Russian)
    • Second Russian edition, revised : Moscow: MCCME, 2014, 584 pp. (with S.P. Novikov) (Russian)
  1. Lectures on Differential Geometry , EMS Series of Lectures in Mathematics, EMS, 2008. 219 pp.
    • Original Russian edition: Moscow-Izhevsk, Institute of Computer Studies, 2002. 176 pp. (Russian)
    • Second edition (revised and expanded): Moscow-Izhevsk, Regular and Chaotic Dynamics, 2006. 260 pp. (Russian)


  1. Quasiclassical approximation for magnetic monopoles.
    Russian Math. Surveys 75:6 (2020) (with Yu.A. Kordyukov)
  2. Trace formula for the magnetic Laplacian.
    Russian Math. Surveys 74:2 (2019), 325-361. (with Yu.A. Kordyukov) [journal]
  3. Discrete analog of the Jacobi set for vector fields.
    Computational Topology in Image Context, 1-11, Lecture Notes in Comput. Sci., 11382, Springer, Cham, 2019. (with A.N. Adilkhanov and A.V. Pavlov) [book]
  4. Darboux-Moutard transformations and Poincare-Steklov operators.
    Proc. Steklov Inst. Math. 302 (2018), 315-324. (with R.G. Novikov)
  5. The generalized Kummer construction and cohomology rings of G_2-manifolds.
    Sb. Math. 209:12 (2018), 1803-1811.
  6. Topological characteristics of digital models of geological core.
    Machine Learning and Knowledge Extraction, 273-281, Lecture Notes in Comput. Sci., 11015, Springer, Cham, 2018. (with R.R. Gilmanov, A.V. Kalyuzhnyuk, and A.A. Yakovlev) [book]
  7. A canonical basis of two-cycles on a K3 surface.
    Sb. Math. 209:8 (2018), 1248-1256.
  8. Topological characteristics of oil and gas reservoirs and their applications.
    Towards Integrative Machine Learning and Knowledge Extraction, 182-193, Lecture Notes in Comput. Sci., 10344, Lecture Notes in Artificial Intelligence, Springer, Cham, 2017. (with V.A. Baikov, R.R. Gilmanov, and A.A. Yakovlev) [book]
  9. The multiplicity problem for periodic orbits of magnetic flows on the 2-sphere.
    Advanced Nonlinear Studies 17 (2017), 17-30. (with A. Abbondandolo, L. Asselle, G. Benedetti, and M. Mazzucchelli) [journal]
  10. On numerical study of the discrete spectrum of a two-dimensional Schrodinger operator with soliton potential.
    Communications in Nonlinear Science and Numerical Simulation 42 (2017), 83-92. (with A.N. Adilkhanov) [journal]
  11. On first integrals of geodesic flows on a two-torus.
    Proc. Steklov Inst. Math. 295 (2016), 225-242. [journal]
  12. The Moutard transformation of two-dimensional Dirac operators and the conformal geometry of surfaces in four-space.
    Math. Notes 100:6 (2016), 835-846. (with R.M. Matuev) [journal]
  13. Moutard-type transform for matrix generalized analytic functions and gauge transforms.
    Russian Math. Surveys 71:5 (2016), 970-972. (with R.G. Novikov) [journal]
  14. The spaces of non-contractible closed curves in compact space forms.
    Sb. Math. 207:10 (2016), 1458-1470. [journal]
  15. On an integrable magnetic geodesic flow on the two-torus.
    Regular and Chaotic Dynamics 20 (2015), 667-678. [journal]
  16. On a higher dimensional generalization of Seifert fibrations.
    Proc. Steklov Inst. Math. 288 (2015), 145-152. [journal]
  17. Blowing up solutions of the modified Novikov-Veselov equation and minimal surfaces.
    Theoret. and Math. Phys. 182:2 (2015), 173-181. [journal]
  18. A fast decaying solution to the modified Novikov-Veselov equation with a one-point singularity.
    Doklady Math. 91 (2015), 145-146. [journal]
  19. The Moutard transformation of two-dimensional Dirac operators and the Mobius geometry.
    Math. Notes 97:1 (2015), 124-135. [journal]
  20. Euclidean minimal tori with planar ends and elliptic solitons.
    Int. Math. Res. Not. IMRN 2015 (2015), no. 14, 5907-5932. (with C. Bohle) [journal]
  21. Two-dimensional von Neumann-Wigner potentials with a multiple positive eigenvalue.
    Functional Anal. Appl. 48:4 (2014), 295-297. (with R.G. Novikov and S.P. Tsarev) [journal]
  22. Spectral curves for Cauchy-Riemann operators on punctured elliptic curves.
    Functional Anal. Appl. 47:4 (2013), 319-322. (with C. Bohle) [journal]
  23. The Moutard transformation and two-dimensional multi-point delta-type potentials.
    Russian Math. Surveys 68:5 (2013), 957-959. (with R.G. Novikov) [journal]
  24. Numerical analysis of topological characteristics of three-dimensional geological models of oil and gas fields.
    Mathematical Modeling 25:10 (2013), 19-31. (Russian) (with Ya.V. Bazaikin, V.A. Baikov, and A.A. Yakovlev) [pdf]
  25. Faddeev eigenfunctions for two-dimensional Schrodinger operators via the Moutard transformation.
    Theoret. and Math. Phys. 176 (2013), 1176-1183. (with S.P. Tsarev) [journal]
  26. On a numerical algorithm for computing topological characteristics of three-dimensional bodies.
    Zh. Vychisl. Mat. Mat. Fiz. 53:4 (2013), 523-530. (Russian) (with Ya.V. Bazaikin) [pdf]
  27. About a role of mean curvature in magnetic mirror geometry.
    Fusion Science and Technology 59t:1 (2011), 190-192. (with A.A. Skovoroda) [journal]
  28. Singular spectral curves in finite gap integration.
    Russian Math. Surveys 66:1 (2011), 107-144. [journal]
  29. Periodic magnetic geodesics on almost every energy level via variational methods.
    Regular and Chaotic Dynamics 15 (2010), 598-605. [journal]
  30. The type numbers of closed geodesics.
    Regular and Chaotic Dynamics 15 (2010), 84100. [journal]
  31. Role of the mean curvature in the geometry of magnetic confinement configurations.
    Plasma Physics Reports 36 (2010), 819-823. (with A.A. Skovoroda) [journal]
  32. The Moutard transformation: an algebraic formalism via pseudodifferential operators and applications.
    OCAMI (Osaka City University Advanced Mathematical Institute) Study Series, V. 3, 2010, pp. 169-183. (with S.P. Tsarev) [pdf]
  33. On the Moutard transformation and its applications to spectral theory and soliton equations.
    J. of Math. Sciences 170 (2010), 371-387. (with S.P. Tsarev) [journal]
  34. Blowing up solutions of the Novikov-Veselov equation.
    Doklady Math. 77 (2008), 467-468. (with S.P. Tsarev) [journal]
  35. Spectral conservation laws for periodic nonlinear equations of the Melnikov type.
    Amer. Math. Soc. Transl. Ser. 2, V. 224, 2008, P. 125-138. (with P.G. Grinevich) [pdf]
  36. Two-dimensional rational solitons and their blow-up via the Moutard transformation.
    Theoret. and Math. Phys. 157 (2008), 1525-1541. (with S.P. Tsarev) [journal]
  37. Surfaces in three-dimensional Lie groups in terms of spinors.
    RIMS Kokyuroku 1605 (2008), 133-150. [pdf]
  38. Two-dimensional Schrodinger operators with fast decaying rational potential and multidimensional L2-kernel.
    Russian Math. Surveys 62:3 (2007), 631-633. (with S.P. Tsarev) [journal]
  39. Infinitesimal Darboux transformations of the spectral curves of tori in the four-space.
    International Mathematics Research Notices 2007 (2007), rnm005, 1-21. (with P.G. Grinevich) [journal]
  40. Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional.
    Siberian Math. J. 48:3 (2007), 395-407. (with D.A. Berdinsky) [journal]
  41. Some algebraic examples of Frobenius manifolds.
    Theoret. and Math. Phys. 151 (2007), 604-613. (with A.E. Mironov) [journal]
  42. Orthogonal curvilinear coordinate systems corresponding to singular spectral curves.
    Proc. Steklov Inst. Math. 255 (2006), 169-184. (with A.E. Mironov) [journal]
  43. Two-dimensional Dirac operator and surface theory.
    Russian Math. Surveys 61:1 (2006), 79-159. [journal]
  44. Surfaces in the four-space and the Davey-Stewartson equations.
    Journal of Geometry and Physics 56 (2006), 1235-1256. [journal]
  45. Surfaces in three-dimensional Lie groups.
    Siberian Math. J. 46:6 (2005), 1005-1019. (with D.A. Berdinsky) [journal]
  46. On the integrability of the n-centre problem.
    Mathematische Annalen 331 (2005), 631--649. (with A. Knauf) [journal]
  47. Finite gap theory of the Clifford torus.
    International Mathematics Research Notices (2005), 103-120. [journal]
  48. Geometric properties of dynamical systems.
    Proceedings of the conference "Mathematics, Mechanics, and Informatics - 2002" dedicated to 10th anniversary of RFBR, Moscow: Fizmatlit, 2005. P. 276-288. [pdf]
  49. The integrability of the n-center problem at high energies.
    Doklady Math. 70 (2004), 502-503. (with A. Knauf) [pdf]
  50. An example of jump from chaos to integrability in magnetic geodesic flows.
    Math. Notes 76 (2004), 587-589. [journal]
  51. Tame integrals of motion and o-minimal structures.
    Amer. Math. Soc. Transl. Ser. 2, V. 212, 2004, P. 317-324. [pdf]
  52. Dirac operators and conformal invariants of tori in the three-space.
    Proc. Steklov Inst. Math. 244 (2004), 233-263. [pdf]
  53. On two-dimensional finite-gap potential Schrodinger and Dirac operators with singular spectral curves.
    Siberian Math. J. 44:4 (2003), 686-694. [journal]
  54. On the formality problem for symplectic manifolds.
    AMS. Contemp. Math., V. 288 (2001), 1-9. (with I.K. Babenko) [pdf]
  55. Integrable geodesic flows on the suspensions of toric automorphisms.
    Proc. Steklov Inst. Math. 231 (2000), 42-58. (with A.V. Bolsinov) [pdf]
  56. Massey products in symplectic manifolds.
    Sb. Math. 191 (2000), 1107-1146. (with I.K. Babenko) [journal]
  57. Integrable geodesic flows with positive topological entropy.
    Inventiones Mathematicae 140 (2000), 639-650. (with A.V. Bolsinov) [journal]
  58. On nonformal simply connected symplectic manifolds.
    Siberian Math. J. 41:2 (2000), 204-217. (with I.K. Babenko) [journal]
  59. An example of an integrable geodesic flow with positive topological entropy.
    Russian Math. Surveys 54:4 (1999), 833-834. (with A.V. Bolsinov) [journal]
  60. Finite-gap solutions of the modified Novikov-Veselov equation, their spectral properties, and applications.
    Siberian Math. J. 40 (1999), 1146-1156. [journal]
  61. The Weierstrass representation of spheres, the Willmore numbers, and soliton spheres.
    Proc. Steklov Inst. Math. 225 (1999), 222-243. [pdf]
  62. A remark on positively curved manifolds of dimensions 7 and 13.
    Tensor and Vector Analysis, Gordon and Breach, Amsterdam, 1998, 282-295. [pdf]
  63. On the existence of nonformal simply connected symplectic manifolds.
    Russian Math. Surveys 53:5 (1998), 1082-1083. (with I.K. Babenko) [journal]
  64. The Weierstrass representation of closed surfaces in R3.
    Functional Anal. Appl. 32:4 (1998), 258-267. [journal]
  65. Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems.
    Trans. Amer. Math. Soc. 350 (1998), 2697-2717. (with A. Bahri) [journal]
  66. Some problems related to topology of manifolds with positive sectional curvature.
    Siberian Adv. Math. 8:4 (1998), 84-108. [pdf]
  67. The global Weierstrass representation and its spectrum.
    Russian Math. Surveys 52:6 (1997), 1330-1332. [journal]
  68. Surfaces of revolution in terms of solitons.
    Ann. Glob. Anal. Geom. 15 (1997), 419-435. [journal]
  69. Secants of abelian varieties, theta functions and soliton equations.
    Russian Math. Surveys 52:1 (1997), 147-218. [journal]
  70. Integrable geodesic flows of non-holonomic metrics.
    Journal of Dynamical Systems and Control Theory 3 (1997), 129-147. [journal]
  71. Difference analogs of the harmonic oscillator.
    Amer. Math. Soc. Transl. Ser. 2, V. 179, 1997, P. 126-130. (with S.P. Novikov) [pdf]
  72. Modified Novikov-Veselov equation and differential geometry of surfaces.
    Amer. Math. Soc. Transl. Ser. 2, V. 179, 1997, P. 133-151. [pdf]
  73. On totally geodesic embeddings of 7-dimensional manifolds into 13-dimensional manifolds of positive sectional curvature.
    Sb. Math. 187 (1996), no. 12, 1853-1867. [journal]
  74. Constant mean curvature surfaces via an integrable dynamical system.
    J. Phys. A : Math. Gen. 29 (1996), 1261-1265. (with B.G. Konopelchenko) [journal]
  75. On the two-gap elliptic potentials.
    Acta Applicandae Math. 36 (1994), 119-124. [journal]
  76. The topology of Riemannian manifolds with integrable geodesic flows.
    Proc. Steklov Inst. Math. 205 (1995), 139-150. [pdf]
  77. Closed geodesics on non-simply connected manifolds.
    Siberian Math. J. 34 (1993), 1154-1160. [journal]
  78. The Landau-Lifshits equation and quadruple secants of Prym varieties.
    Functional Anal. Appl. 27 (1993), 222-224. [journal]
  79. Closed non-self-intersecting extremals of multivalued functionals.
    Siberian Math. J. 33 (1992), 686-692. [journal]
  80. On the existence of three nonintersecting closed geodesics on manifolds that are homeomorphic to the two-dimensional sphere.
    Russian Acad. Sci. Izv. Math. 40 (1993), 565-590. [journal]
  81. Closed extremals on two-dimensional manifolds.
    Russian Math. Surveys 47:2 (1992), 163-211. [journal]
  82. Non-self-intersecting closed extremals of multivalued or not-everywhere-positive functionals.
    Math. USSR-Izv. 38 (1992), 359-374. [pdf]
  83. Prym theta functions and hierarchies of nonlinear equations.
    Math. Notes 50 (1992), 723-730. [journal]
  84. Prym varieties of branched coverings, and nonlinear equations.
    Math. USSR-Sb. 70 (1991), 367-384. [pdf]
  85. Two-dimensional finite-zone Schrodinger potential operators.
    Functional Anal. Appl. 24 (1990), no. 1, 76-77. [journal]
  86. Elliptic solutions of nonlinear equations.
    Theoret. and Math. Phys. 84 (1991), 700-706. [journal]
  87. Multivalued finite-zone solutions of the equation D u = sin u.
    Math. Notes 47 (1990), 293-297. [journal]
  88. Smooth real finite-zone solutions of sine-Gordon type equations.
    Math. Notes 47 (1990), 94-100. [journal]
  89. On topological properties of integrable geodesic flows.
    Mathematical Notes 44:2 (1988), 283-284. (Russian) [pdf]
  90. Topological obstructions to the integrability of geodesic flows on nonsimply connected manifolds.
    Math. USSR-Izv. 30 (1988), 403-409. [pdf]
  91. On an analogue of the Novikov conjecture in a problem of Riemann-Schottky type for Prym varieties.
    Sov. Math. Dokl. 35 (1987), 420-424. [pdf]
  92. Effectivization of theta-function formulas for two-dimensional Schrodinger potential operators that are finite-gap at a certain energy level.
    Sov. Math. Dokl. 32 (1985), 843-846. [pdf]
  93. Closed geodesics on non-simply-connected manifolds.
    Russian Math. Surveys 40:6 (1986), 143-144. [pdf]
  94. Periodic extremals of multivalued or not everywhere positive functionals.
    Sov. Math. Dokl. 29 (1984), 18-20. (with S.P. Novikov) [pdf]
  95. The principle of throwing out cycles in Morse-Novikov theory.
    Sov. Math. Dokl. 27 (1983), 43-46. [pdf]