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Real hypersurfaces of the Jacobi operator with respect to the structure vector field in a complex space form

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Abstract

We study a real hypersurface $M$ satisfying $L_\xi S = 0$ and $R_\xi S = SR_\xi$ in a complex hyperbolic space $H_n{\Bbb C}$, where $S$ is the Ricci tensor of type (1,1) on $M$, $L_\xi$ and $R_\xi$ denotes the operator of the Lie derivative and the Jacobi operator with respect to the structure vector field $\xi$ respectively

참고문헌 (7)

  1. "\ref \key 12 \bysame \paper On real hypersurfaces of a complexprojective space \jour Math. Z. \vol 202 \yr 1989 \pages 299--311\endref"
  2. "\ref \key 13\by S. Maeda\paper Ricci tensors of real hypersurfacesin a complex projective space \jour Proc. Amer. Math. Soc.\vol122\yr 1994 \pages 1229--1235\endref"
  3. "\ref \key 14\by S. Montiel\paper Real hypersurfaces of a complexhyperbolic space \jour J. Math. Soc. Japan\vol 37\yr 1985\pages515--535\endref"
  4. "\ref \key 15 \by S. Montiel and A. Romero\paper On some realhypersurfaces of a complex hyperbolic space \jour Geom.Dedicata\vol 20 \yr 1986 \pages 245--261\endref"
  5. "\ref \key 16\by R. Niebergal and P.~J. Ryan \paper Real hypersurfaces in complex space forms", in Tight and Tautsubmanifolds \jour Cambridge Univ. Press
  6. "\ref \key 17 \by R. Takagi \paper On homogeneous realhypersurfaces of a complex projective space\jour Osaka J. Math. \vol 10 \yr 1973 \pages 495--506\endref"
  7. "\ref \key 18\bysame \paper Real hypersurfaces in a complexprojective space with constant principal curvatures I", pp.507~

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