# CERTAIN CONTACT CR-SUBMANIFOLDS OF AN ODD-DIMENSIONAL UNIT SPHERE

• Kim, Hyang-Sook (Department of Computational Mathematics School of Computer Aided Science and Institute of Mathematical Sciences College of Natural Science Inje University) ;
• Pak, Jin-Suk (Department of Mathematics Education Kyungpook National University)
• Published : 2007.02.28
• 70 13

#### Abstract

We study an (n+1)($(n{\geq}3)$-dimensional contact CR-submanifold of (n-1) contact CR-dimension in a (2m+1)-unit sphere $S^{2m+1}$, and to determine such sub manifolds under conditions concerning the second fundamental form and the induced almost contact structure.

#### Keywords

odd-dimensional unit sphere;contact CR-submanifold;Sasakian structure;almost contact structure

#### References

1. B. Y. Chen, Geometry of submanifolds, Marcel Dekker Inc., New York, 1973
2. J. Erbacher, Reduction of the codimension of an isometric immersion, J. Diff. Geom. 5 (1971), 333-340 https://doi.org/10.4310/jdg/1214429997
3. M. Kon, On hypersurfaces immersed in $S^{2n+1}$, Ann. Fac. Aci. de Kinshasa 4 (1978), 1-24
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. P. Ryan, Homogeneity and some curvature condition for hypersurfaces, Tohoku J. Math. 21 (1969), 363-388 https://doi.org/10.2748/tmj/1178242949
6. K. Yano and M. Kon, CR submanifolds of Kaehlerian and Sasakian manifolds, Birkhauser, Boston-Basel-Stuttgart, 1983
7. A. Bejancu, Geometry of CR-submanifolds, D. Reidel Publishing Company, Dordrecht-Boston-Lancaster-Tokyo, 1986
8. J. S. Pak, J.-H. Kwon, H. S. Kim, and Y.-M. Kim, Contact CR-submanifolds of an odd-dimensional unit sphere, Geometriae Dedicata 114 (2005), 1-11 https://doi.org/10.1007/s10711-004-8175-9

#### Cited by

1. CERTAIN CLASS OF CONTACT CR-SUBMANIFOLDS OF A SASAKIAN SPACE FORM vol.29, pp.1, 2014, https://doi.org/10.4134/CKMS.2014.29.1.131
2. 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