Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE RICCI CURVATURE OF SUBMANIFOLDS IN THE WARPED PRODUCT L × f F

  • Kim, Young-Mi (Department of Mathematics Kyungpook National University Taegu 702-701) ;
  • Pak, Jin-Suk (Department of Mathematics Kyungpook National University Taegu 702-701)
  • Published : 2002.09.01
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Abstract

The warped product L$\times$$_{f}$ F of a line L and a Kaehler manifold F is a typical example of Kenmotsu manifold. In this paper we determine submanifolds of L$\times$$_{f}$ F which are tangent to the structure vector field and satisfy certain conditions concerning with Ricci curvature and mean curvature.ure.

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References

  1. Lecture Note in Mathematics v.509 Contact manifolds in Riemannian geometry Matsumoto D. E. Blair
  2. Arch Math v.60 Some pinching and classification theorems for minimal submanifolds B.Y. Chen https://doi.org/10.1007/BF01236084
  3. Geometry and topology of submanifolds v.6 A Riemannian invariant for submanifold in space forms and its applications B. Y. Chen
  4. Results Math v.27 A Riemannian invariant and its applications to submanifold theory B. Y. Chen https://doi.org/10.1007/BF03322265
  5. Glasg. Math. J. v.41 Relations between Ricci curvature and shape operator for submanifolds with arbistrary codimension B. Y. Chen https://doi.org/10.1017/S0017089599970271
  6. On submanifolds of L × fF satisfying Chen's basic equality(preprint) S. Funabashi;Y. -M. Kim;J. S. Pak
  7. Tohoku Math. J. v.24 A class of almost sontact Riemannian manifolds K. Kenmotsu https://doi.org/10.2748/tmj/1178241594
  8. Houston J. Math. v.25 A basic inequality for sunmanifolds in Sasakian space forms Y. H. Kim;D.-S. Kim
  9. Lecture Note Almost contact manidolds S. Sasaki
  10. Tohoku Math. J. v.21 The automorphism groups of almost contact Riemannian manidolds S. Tanno https://doi.org/10.2748/tmj/1178243031
  11. CR submanifolds of Kaehlerian and Sasakian manifolds K. Yano;M. Kon

Cited by

  1. ON CONTACT SLANT SUB MANIFOLD OF L ×fF vol.19, pp.1, 2004, https://doi.org/10.4134/CKMS.2004.19.1.129