Lobachevskii Journal of Mathematics

, Volume 39, Issue 1, pp 20–24 | Cite as

A Note on Geometry of Special Hermitian Manifolds



It is proved that the almost contact metric structures on totally geodesic and 1-type hypersurfaces in special Hermitian manifolds have identical properties.

Keywords and phrases

almost contact metric structure hypersurface special Hermitian manifold 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Abu-Saleem and M. B. Banaru, “Two theorems on Kenmotsu hypersurfaces in a W 3-manifold,” Studia Univ. Babeş-Bolyai.Math. 51 (3), 3–11 (2005).MATHGoogle Scholar
  2. 2.
    A. Abu-Saleem and M. B. Banaru, “Some applications of Kirichenko tensors,” An. Univ. Oradea, Fasc.Mat. 17 (2), 201–208 (2010).MathSciNetMATHGoogle Scholar
  3. 3.
    A. Abu-Saleem and M. B. Banaru, “On almost contact metric hypersurfaces of nearly Kählerian 6-sphere,” Malays. J. Math. Sci. 8 (1), 35–46 (2014).MathSciNetGoogle Scholar
  4. 4.
    M. B. Banaru, “Two theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of Cayley algebra,” J. Harbin Inst. Technol. 8 (1), 38–40 (2001).MathSciNetMATHGoogle Scholar
  5. 5.
    M. B. Banaru, “A note on six-dimensional G 1-submanifolds of octave algebra,” Taiwanese J. Math. 6 (3), 383–388 (2002).MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    M. B. Banaru, “On minimality of a Sasakian hypersurface in a W 3-manifold,” Saitama Math. J. 20, 1–7 (2002).MathSciNetMATHGoogle Scholar
  7. 7.
    M. B. Banaru, “On W3-manifolds satisfying G-cosymplectic hypersurfaces axiom,” in Proceedings of the 24th Young Scientists Conference atMoscow State University, Moscow, 2002 (Moscow, 2002), pp. 13–15.Google Scholar
  8. 8.
    M. B. Banaru, “On Sasakian hypersurfaces in 6-dimensional Hermitian submanifolds of the Cayley algebra,” Sb.: Math. 194 (8), 1125–1137 (2003).MathSciNetMATHGoogle Scholar
  9. 9.
    M. B. Banaru, “On the Kenmotsu hypersurfaces of special Hermitian manifolds,” Sib. Math. J. 45 (1), 7–10 (2004).CrossRefMATHGoogle Scholar
  10. 10.
    M. B. Banaru, “SpecialHermitian manifolds and the 1-cosymplectic hypersurfaces axiom,” Bull. Aust.Math. Soc. 90 (3), 504–509 (2014).MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    M. B. Banaru, “Geometry of 6-dimensional Hermitian manifolds of the octave algebra,” J. Math. Sci. 207 (3), 354–388 (2015).CrossRefMATHGoogle Scholar
  12. 12.
    M. B. Banaru, “On almost contact metric 1-hypersurfaces in Kählerian manifolds,” Sib. Math. J. 55 (4), 585–588 (2014).MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    M. B. Banaru, “The axiom of Sasakian hypersurfaces and six-dimensional Hermitian submanifolds of the octonion algebra,” Math. Notes 99 (1), 155–159 (2016).MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    M. Banaru and V. F. Kirichenko, “Almost contact metric structures on the hypersurface of almost Hermitian manifolds,” J.Math. Sci. 207 (4), 513–537 (2015).CrossRefMATHGoogle Scholar
  15. 15.
    D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics (Birkhäuser, Boston, Basel, Berlin, 2002).CrossRefMATHGoogle Scholar
  16. 16.
    A. Gray and L. M. Hervella, “The sixteen classes of almost Hermitian manifolds and their linear invariants,” Ann.Mat. Pure Appl. 123 (4), 35–58 (1980).MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    V. F. Kirichenko, “Sur la gèomètrie des variètès approximativement cosymplectiques,” C. R. Acad. Sci. Paris, Ser. 1 295, 673–676 (1982).MATHGoogle Scholar
  18. 18.
    V. F. Kirichenko, Differential-Geometrical Structures on Manifolds (Pechatnyi Dom, Odessa, 2013) [in Russian].Google Scholar
  19. 19.
    H. Kurihara, “The type number on real hypersurfaces in a quaternionic space form,” Tsukuba J. Math. 24, 127–132 (2000).MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Gh. Pitiş, Geometry of Kenmotsu Manifolds (Transilvania Univ. Press, Brašov, 2007).MATHGoogle Scholar
  21. 21.
    L. V. Stepanova and M. B. Banaru, “On hypersurfaces of quasi-Kählerian manifolds,” An. Ştinţ. Univ. Al. I. Cuza din laši. Ser. NouăMat. 47 (1), 65–70 (2001).MATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Smolensk State UniversitySmolenskRussia

Personalised recommendations