Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

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
Download PDF
⟨ Previous Next ⟩

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

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. M. Kon, On hypersurfaces immersed in $S^{2n+1}$, Ann. Fac. Aci. de Kinshasa 4 (1978), 1-24
  5. 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
  6. 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
  7. P. Ryan, Homogeneity and some curvature condition for hypersurfaces, Tohoku J. Math. 21 (1969), 363-388 https://doi.org/10.2748/tmj/1178242949
  8. K. Yano and M. Kon, CR submanifolds of Kaehlerian and Sasakian manifolds, Birkhauser, Boston-Basel-Stuttgart, 1983

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