Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-06T00:23:01.039Z Has data issue: false hasContentIssue false
  • English
  • Français

Certain inequalities for submanifolds in (K,μ)-contact space forms

Published online by Cambridge University Press:  17 April 2009

Kadri Arslan ,
Ridvan Ezentas ,
Ion Mihai ,
Cengizhan Murathan  and
Cihan Özgür
Kadri Arslan
Affiliation:
Uludag University, Department of Mathematics, Göorükle 16059, Bursa, Turkey
Ridvan Ezentas
Affiliation:
Uludag University, Department of Mathematics, Göorükle 16059, Bursa, Turkey
Ion Mihai
Affiliation:
Faculty of Mathematics, Str. Academiei 14, 70109 Bucharest, Romania
Cengizhan Murathan
Affiliation:
Uludag University, Department of Mathematics, Göorükle 16059, Bursa, Turkey
Cihan Özgür
Affiliation:
Uludag University, Department of Mathematics, Göorükle 16059, Bursa, Turkey
Rights & Permissions [Opens in a new window]

Extract

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.

Chen (1999) established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemanian space form with arbitrary codimension. Matsumoto (to appear) dealt with similar problems for sub-manifolds in complex space forms.

In this article we obtain sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in (K, μ)-contact space forms.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 201 - 212
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Blair, D.E., Contact manifolds in Riemannian heometry, Lecture Notes in Math. 509 (Springer-Verlag, Berlin, Heidelberg, New York, 1976).CrossRefGoogle Scholar
[2]Blair, D., Koufogiorgos, T. and Papantoniou, B.J., ‘Contact metric manifolds satisfying a nullity condition’, Israel J.Math. 91 (1995), 189–214.CrossRefGoogle Scholar
[3]Chen, B.Y., ‘Some pinching and classification theorems for minimal submanifolds’, Arch. Math. 60 (1993), 568–578.CrossRefGoogle Scholar
[4]Chen, B. Y., ‘Some new obstructions to minimal and Lagrangian isometric immersions’, Japan. J. Math. 26 (2000), 105–127.CrossRefGoogle Scholar
[5]Chen, B.Y., ‘Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimensions’, Glasgow Math. J. 41 (1999), 33–41.CrossRefGoogle Scholar
[6]Defever, F., Mihai, I. and Verstraelen, L., ‘B.Y.Chen's inequality for C-totally real sub-manifolds in Sasakian space forms’, Boll. Un. Mat. Ital. 11 (1997), 365–374.Google Scholar
[7]Koufogiorgos, T., ‘Contact Riemannian manifolds with constant ϕ-sectional curvature’, in Geometry and topology of submanifolds 8 (World Scientific, Singapore, 1995), pp. 195–197.Google Scholar
[8]Mihai, I., ‘Ricci curvature of submanifolds in Sasakian space forms’, J. Austral. Math. Soc. (to appear).Google Scholar