SCALAR CURVATURE OF CONTACT CR-SUBMANIFOLDS IN AN ODD-DIMENSIONAL UNIT SPHERE

Title & Authors
SCALAR CURVATURE OF CONTACT CR-SUBMANIFOLDS IN AN ODD-DIMENSIONAL UNIT SPHERE
Kim, Hyang-Sook; Pak, Jin-Suk;

Abstract
In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere $\small{S^{2m+1}}$. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.
Keywords
Sasakian manifold;odd-dimensional unit sphere;contact CR-submanifold;scalar curvature;
Language
English
Cited by
1.
HOMOLOGY OF CONTACT CR-WARPED PRODUCT SUBMANIFOLDS OF AN ODD-DIMENSIONAL UNIT SPHERE,;;

대한수학회보, 2015. vol.52. 1, pp.215-222
1.
HOMOLOGY OF CONTACT CR-WARPED PRODUCT SUBMANIFOLDS OF AN ODD-DIMENSIONAL UNIT SPHERE, Bulletin of the Korean Mathematical Society, 2015, 52, 1, 215
References
1.
A. Bejancu, Geometry of CR-Submanifolds, D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1886.

2.
B. Y. Chen, Geometry of Submanifolds, Marcel Dekker Inc., New York, 1973.

3.
M. Djoric and M. Okumura, The scalar curvature of CR submanifolds of maximal CR dimension of complex projective space, Monatsh. Math. 154 (2008), no. 1, 11-17.

4.
J. Erbacher, Reduction of the codimension of an isometric immersion, J. Differential Geometry 5 (1971), 333-340.

5.
H. S. Kim and J. S. Pak, Certain contact CR-submanifolds of an odd-dimensional unit sphere, Bull. Korean Math. Soc. 44 (2007), no. 1, 109-116.

6.
H. S. Kim and J. S. Pak, Certain class of contact CR-submanifolds of an odd-dimensional unit sphere, to appear in Taiwanese Math. J.

7.
H. S. Kim and J. S. Pak, Scalar curvature of QR-submanifolds with maximal QR-dimension in a quaternionic projective space, submitted.

8.
M. Kon, On hypersurfaces immersed in \${S^{2n+1}\$, Ann. Fac. Sci. Univ. Nat. Zaıre (Kinshasa) Sect. Math.-Phys. 4 (1978), no. 1, 1-24.

9.
J.-H. Kwon and J. S. Pak, On some contact CR-submanifolds of an odd-dimensional unit sphere, Soochow J. Math. 26 (2000), no. 4, 427-439.

10.
J. S. Pak, J.-H. Kwon, H. S. Kim, and Y.-M. Kim, Contact CR-submanifolds of an odd-dimensional unit sphere, Geom. Dedicata 114 (2005), 1-11.

11.
K. Yano, Integral Formulas in Riemannian Geometry, Pure and Applied Mathematics, No. 1 Marcel Dekker, Inc., New York 1970.

12.
K. Yano and M. Kon, CR Submanifolds of Kaehlerian and Sasakian Manifolds, Progress in Mathematics, 30. Birkhauser, Boston, Mass., 1983.