Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-23T21:35:48.907Z Has data issue: false hasContentIssue false
  • English
  • Français

SPECIAL HERMITIAN MANIFOLDS AND THE 1-COSYMPLECTIC HYPERSURFACES AXIOM

Part of: Local differential geometry

Published online by Cambridge University Press:  15 May 2014

MIHAIL B. BANARU
MIHAIL B. BANARU*
Affiliation:
Chair of Mathematics and Informatics, Smolensk State University, Przhevalski str., 4, Smolensk 214 000,Russian Federation email [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is proved that if a special Hermitian manifold complies with the 1-cosymplectic hypersurfaces axiom, then it is a Kählerian manifold.

Keywords

almost contact metric structurecosymplectic structurespecial Hermitian manifoldKählerian manifoldtype number

MSC classification

Secondary: 53B35: Hermitian and Kählerian structures 53B50: Applications to physics
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 90 , Issue 3 , December 2014 , pp. 504 - 509
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

References

Abu-Saleem, A. and Banaru, M., ‘Some applications of Kirichenko tensors’, An. Univ. Oradea Fasc. Mat. 17 (2010), 201–208.Google Scholar
Banaru, M., ‘Two theorems on cosymplectic hypersurfaces of six-dimensional Hermitian submanifolds of Cayley algebra’, J. Harbin Inst. Tech. 8 (2000), 38–40.Google Scholar
Banaru, M., ‘A note on six-dimensional G 1-submanifolds of octave algebra’, Taiwanese J. Math. 6 (2002), 383–388.Google Scholar
Banaru, M., ‘On $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}W_3$-manifolds satisfying G-cosymplectic hypersurfaces axiom’, Proc. XXIV Young Scientists Conf., Moscow State University, 2002, 13–15 (in Russian).Google Scholar
Banaru, M., ‘On minimality of a Sasakian hypersurface in a W 3-manifold’, Saitama Math. J. 20 (2002), 1–7.Google Scholar
Banaru, M., ‘Hermitian manifolds and U-cosymplectic hypersurfaces axiom’, J. Sichuan Univ. Nat. Sci. 26 (2003), 261–263.Google Scholar
Banaru, M., ‘On the type number of six-dimensional planar Hermitian submanifolds of Cayley algebra’, Kyungpook Math. J. 43 (2003), 27–35.Google Scholar
Banaru, M., ‘On the Gray–Hervella classes of AH-structures on six-dimensional submanifolds of Cayley algebra’, Annuaire Univ. Sofia Fac. Math. Inform. 95 (2004), 125–131.Google Scholar
Blair, D. E., ‘Riemannian geometry of contact and symplectic manifolds’, Progress in Mathematics (Birkhauser, Boston–Basel–Berlin, 2002).Google Scholar
Gray, A. and Hervella, L. M., ‘The sixteen classes of almost Hermitian manifolds and their linear invariants’, Ann. Mat. Pura Appl. (4) 123 (1980), 35–58.CrossRefGoogle Scholar
Kholodenko, A. L., Applications of Contact Geometry and Topology in Physics (World Scientific, New Jersey–London–Singapore, 2013).Google Scholar
Kirichenko, V. F., ‘Sur la gèomètrie des varietes approximativement cosymplectiques’, C. R. Acad. Sci. Paris Ser. 1 295 (1982), 673–676.Google Scholar
Kirichenko, V. F., Differential–Geometrical Structures on Manifolds (MSPU, Moscow, 2003) (in Russian).Google Scholar
Kurihara, H., ‘The type number on real hypersurfaces in a quaternionic space form’, Tsukuba J. Math. 24 (2000), 127–132.Google Scholar