# SECTIONAL CURVATURE OF CONTACT C R-SUBMANIFOLDS OF AN ODD-DIMENSIONAL UNIT SPHERE

• Kim, Hyang-Sook (DEPARTMENT OF COMPUTATIONAL MAHEMATICS, SCHOOL OF COMPUTER AIDED SCIENCE, INJE UNIVERSITY) ;
• Pak, Jin-Suk (DEPARTMENT OF MATHEMATICS, KYUNGPOOK NATINAL UNIVERSITY)
• Published : 2005.11.01

#### Abstract

In this paper we study (n + 1)-dimensional compact contact CR-submanifolds of (n - 1) contact CR-dimension immersed in an odd-dimensional unit sphere $S^{2m+1}$. Especially we provide necessary conditions in order for such a sub manifold to be the generalized Clifford surface $$S^{2n_1+1}(((2n_1+1)/(n+1))^{\frac{1}{2}})\;{\times}\;S^{2n_2+1}(((2n_2+1)/(n+1)^{\frac{1}{2}})$$ for some portion (n1, n2) of (n - 1)/2 in terms with sectional curvature.

#### References

1. A. Bejancu, Geometry of CR-submanifolds, D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1986
2. B. Y. Chen, Geometry of submanifolds, Marcel Dekker Inc., New York, 1973
3. J. Erbacher, Reduction of the codimension of an isometric immersion, J. Differential Geom. 5 (1971), 333-340 https://doi.org/10.4310/jdg/1214429997
4. J.-H. Kwon and J. S. Pak, On some contact CR-submanifolds of an odd-dimensional unit sphere, Soochow J. Math. 26 (2000), 427-439
5. J. S. Pak, J.-H. Kwon, H. S. Kim, and Y.-M. Kim, Contact CR-submanifolds of an odd-dimensional unit sphere, accepted in Geom. Dedicata
6. P. J. Ryan, Homogeneity and some curvature conditions for hypersurfaces, Tohoku Math. J. 21 (1969), 363-388 https://doi.org/10.2748/tmj/1178242949
7. K. Yano and M. Kon, CR submanifolds of Kaehlerian and Sasakian manifolds, Birkhauser, Boston, Basel, Stuttgart, 1983

#### Cited by

1. HOMOLOGY OF CONTACT CR-WARPED PRODUCT SUBMANIFOLDS OF AN ODD-DIMENSIONAL UNIT SPHERE vol.52, pp.1, 2015, https://doi.org/10.4134/BKMS.2015.52.1.215