Hostname: page-component-7dd5485656-bt4hw Total loading time: 0 Render date: 2025-10-31T09:39:53.448Z Has data issue: false hasContentIssue false
  • English
  • Français

C-totally real submanifolds in (κ,μ)-contact space forms

Published online by Cambridge University Press:  17 April 2009

Mukut Mani Tripathi  and
Jeong-Sik Kim
Mukut Mani Tripathi
Affiliation:
Department of Mathematics and Astronomy, Lucknow University, Lucknow 226 007, India, e-mail: mm-tripathi@hotmail.com
Jeong-Sik Kim
Affiliation:
Department of Mathematics education, Sunchon National University, Sunchon 540-742, Korea, e-mail: jskim01@hanmir.com
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.

We obtain a basic B,-Y. Chen's inequality for a C-totally real submanifold in a (κ,μ)-contact space form involving intrinsic invariants, namely the scalar curvature and the sectional curvatures of the submanifold on left hand side and the main extrinsic invariant, namely the squared mean curvature on the right hand side. Inequalities between the squared mean curvature and Ricci curvature and between the squared mean curvature and κ-Ricci curvature are also obtained. These results are applied to get corresponding results for C-totally real submanifolds in a Sasakian space form.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 51 - 65
Copyright
Copyright © Australian Mathematical Society 2003

References

REFERENCES

[1]Arnold, V.I., ‘Contact geometry: the geometrical method of Gibb's thermodynamics’,in Proceedings of the Gibbs Symposium, Yale University,(May 15–17, 1989) (American Mathematical society, Providence R.I., 1990), PP. 163–179.Google Scholar
[2]Arslan, K., Ezentas, R., Mihai, I., Murathan, C. and Ozgur, C., ‘Certain inequalities for submanifolds in (κ,μ)-contact space forms’, Bull. Austral. Math. Soc. 64 (2001), 201–212.CrossRefGoogle Scholar
[3]Blair, D.E., Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics 509 (Springer Verlag, Berlin, New York, 1976).CrossRefGoogle Scholar
[4]Blair, D.E., Koufogiorgos, T. and Papantonion, B.J., ‘Contact metric manifolds satisfying a nullity condition’, Israel J. Math. 91 (1995), 189–214.CrossRefGoogle Scholar
[5]Chen, B.-Y., ‘Some pinching and classification theorems for minimal submanifolds’, Arch. Math. (Basel) 60 (1993), 568–578.CrossRefGoogle Scholar
[6]Chen, B.-Y., ‘A general inequality for submanifolds in complex-space-forms and its applications’, Arch. Math. (Basel) 67 (1996), 519–528.CrossRefGoogle Scholar
[7]Chen, B.-Y., ‘Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions’, Glasgow Math. J. 41 (1999), 33–41.CrossRefGoogle Scholar
[8]Chen, B.-Y., ‘Riemannian submanifolds’, in Handbook of Differential Geometry, (Dillen, F. and Verstraelen, L., Editors) (North Holland, Amsterdam, 2000), PP. 187–418.Google Scholar
[9]Defever, F., Mihai, I. and Verstraelen, L., ‘B.-Y. Chen's inequalities for C-totally real submanifolds of Sasakian space forms’, Boll. Un. Mat.Ital. B (7) 11 (1997), 365–374.Google Scholar
[10]Geiges, H., ‘A brief history of contact geometry and topology’, Exposition. Math. 19 (2001), 25–53.CrossRefGoogle Scholar
[11]Koufogiorgos, T., ‘Contact Riemannian manifolds with constant ϕ-sectional curvature’, Tokyo J. Math. 20 (1997), 13–22.CrossRefGoogle Scholar
[12]Tripathi, M.M. and Shukla, S.S., ‘When is a submanifold of a Sasakian manifold anti-invariant?’, in Geometry, analysis and applications (Varanasi, 2000) (World Sci. Publishing, River Edge, NJ, 2001), PP. 145–153.Google Scholar
[13]Yamaguchi, S., Kon, M. and Ikawa, T., ‘C-totally real submanifolds’, J. Differential Geom. 11 (1976), 59–65.CrossRefGoogle Scholar
[14]Yano, K. and Kon, M., Anti-invariant submanifolds, Lecture Notes in Pure and Applied Mathematics 21 (Marcel Dekker, Inc., New York, Basel, 1976).Google Scholar