JOURNAL BROWSE
Search
Advanced SearchSearch Tips
SCALAR CURVATURE OF CONTACT THREE CR-SUBMANIFOLDS IN A UNIT (4m + 3)-SPHERE
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
SCALAR CURVATURE OF CONTACT THREE CR-SUBMANIFOLDS IN A UNIT (4m + 3)-SPHERE
Kim, Hyang-Sook; Pak, Jin-Suk;
  PDF(new window)
 Abstract
In this paper we derive an integral formula on an (n + 3)-dimensional, compact, minimal contact three CR-submanifold M of (p-1) contact three CR-dimension immersed in a unit (4m+3)-sphere . Using this integral formula, we give a sufficient condition concerning the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.
 Keywords
unit (4m+3)-sphere;Sasakian 3-structure;contact three CR-submanifold;scalar curvature;
 Language
English
 Cited by
 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. Diff. Geom. 5 (1971), 333-340.

4.
S. Ishihara and M. Konish, Differential geometry of fibred spaces, Study Group of Differential Geometry, Tokyo, 1973.

5.
T. Kashiwada, A note on a Riemannian space with Sasakian 3-structure,Natur. Sci. Rep. Ochanomizu Univ. 22 (1971), 1-2.

6.
Y. Y. Kuo On almost contact 3-structure, Tohoku Math. J. 22 (1970), 325-332. crossref(new window)

7.
J.-H. Kwon and J. S. Pak, On contact three CR-submanifolds of a (4m+3)-dimensional unit sphere, Comm. Korean Math Soc. 13 (1998), no. 3, 561-577.

8.
J. S. Pak, Real hypersurfaces in quaternionic Kaehlerian manifolds with constant Qsectional curvature, Kodai Math. Sem. Rep. 29 (1977), no. 1-2, 22-61. crossref(new window)

9.
K. Yano, Integral formulas in Riemannian geometry, Marcel Dekker Inc., New York, 1970.

10.
K. Yano and M. Kon, CR submanifolds of Kaehlerian and Sasakian manifolds, Birkhauser, Boston-Basel-Stuttgart, 1983.