DOI QR코드

DOI QR Code

SCALAR CURVATURE OF CONTACT THREE CR-SUBMANIFOLDS IN A UNIT (4m + 3)-SPHERE

  • Kim, Hyang-Sook (Department of Computational Mathematics School of Computer Aided Science Institute of Basic Science Inje University) ;
  • Pak, Jin-Suk (Graduate School of Education Daegu University)
  • Received : 2009.09.29
  • Published : 2011.05.31

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 $S^{4m+3}$. 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.

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. https://doi.org/10.4310/jdg/1214429997
  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. https://doi.org/10.2748/tmj/1178242759
  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. https://doi.org/10.2996/kmj/1138833571
  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.