Journal of Mathematical Sciences

, 177:668 | Cite as

On geometry of weakly cosymplectic manifolds



We consider classes of weakly cosymplectic manifolds whose Riemannian curvature tensors satisfy contact analogs of the Riemannian–Christoffel identities. Additional properties of the Riemannian curvature tensor symmetry are found and a classification of weakly cosymplectic manifolds is obtained.


Manifold Contact Structure Structure Tensor Ahlerian Manifold Contact Manifold 


  1. 1.
    D. E. Blair, “Almost contact manifolds with Killing structure tensors,” Pac. J. Math., 39, No. 2, 285–292 (1971).MathSciNetMATHGoogle Scholar
  2. 2.
    D. E. Blair and D. K. Showders, “Almost contact manifolds with Killing structure tensors,” J. Differ. Geom., 9, 577–582 (1974).MATHGoogle Scholar
  3. 3.
    A. Gray, “Nearly Kählerian manifolds,” J. Differ. Geom., 4, No. 3, 283–309 (1970).MATHGoogle Scholar
  4. 4.
    A. Gray, “Curvature identities for Hermitian and almost Hermitian manifolds,” Tôhoku Math. J., 28, 601–612 (1976).MATHCrossRefGoogle Scholar
  5. 5.
    V. F. Kirichenko, “K-spaces of constant holomorphic sectional curvature,” Mat. Zametki, 9, 805–814 (1976).Google Scholar
  6. 6.
    V. F. Kirichenko, “Sur le géométrie des variétés approximativent cosymplectiques,” C. R. Acad. Sci. Paris, 295, 673–676 (1982).MATHGoogle Scholar
  7. 7.
    V. F. Kirichenko, “Methods of generalized Hermitian geometry in the theory of almost contact manifolds,” Itogi Nauki Tekhn. Ser. Probl. Geom. Tr. Geom. Sem., 18, 25–71 (1986).MathSciNetGoogle Scholar
  8. 8.
    V. F. Kirichenko, “Generalized quasi-K¨ahlerian manifolds and axioms of CR-submanifolds in generalized Hermitian geometry, II,” Geom. Dedicata, 52, 53–85 (1994).MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    V. F. Kirichenko, Differential-Geometric Structures on Manifolds [in Russian], MPGU, Moscow (2003).Google Scholar
  10. 10.
    V. F. Kirichenko and O. E. Arsenyeva, Introduction to Modern Geometry [in Russian], Tver State Univ., Tver (1997).Google Scholar
  11. 11.
    V. F. Kirichenko and I. P. Borisovsky, “Integral manifolds of contact distributions,” Mat. Sb., 189, No. 12, 119–134 (1998).Google Scholar
  12. 12.
    V. F. Kirichenko and L. V. Lipagina, “Killing f-manifolds of constant type,” Izv. Ross. Akad. Nauk, Ser. Mat., 63, No. 5, 127–146 (1999).MathSciNetGoogle Scholar
  13. 13.
    V. F. Kirichenko and A. R. Rustanov, “Differential geometry of quasi-Sasakian manifolds,” Mat. Sb., 193, No. 8, 71–100 (2002).MathSciNetGoogle Scholar
  14. 14.
    S. Kobayashi and K. Nomidzu, Foundations of Differential Geometry [Russian translation], Vol. 1, Nauka, Moscow (1981).Google Scholar
  15. 15.
    S. Kobayashi and K. Nomidzu, Foundations of Differential Geometry [Russian translation], Vol. 2, Nauka, Moscow (1981).Google Scholar
  16. 16.
    H. Proppe, Almost Contact Hypersurfaces of Certain Almost Complex Manifolds, Ph.D. Thesis, McGill Univ. (1969).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Moscow Pedagogical State UniversityMoscowRussia

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