The structure Jacobi operator and the shape operator of real hypersurfaces in CP^{2} and CH^{2}

K. Panagiotidou

The structure Jacobi operator and the shape operator of real hypersurfaces in CP^{2} and CH^{2}

Differential Geometry 2012-09-10 v1

Authors: K. Panagiotidou

Abstract

This paper presents two results conserning real hypersurfaces in CP^{2} and CH^{2}. More precisely, it is proved that real hypersurfaces equipped with structure Jacobi operator satisfying condition $\mathcal{L}_{X}l=\nabla_{X}l$ , where \emph{X} is a vector field orthogonal to structure vector field $\xi$ , do not exist. Additional real hypersurfaces equipped with shape operator \emph{A} satisfying relation $\mathcal{L}_{X}A=\nabla_{X}A$ , where \emph{X} is a vector field orthogonal to $\xi$ , do not exist.

Keywords

real hypersurfaces complex projective space complex hyperbolic space structure jacobi operator shape operator lie derivative covariant derivative

Cite

@article{arxiv.1209.0131,
  title  = {The structure Jacobi operator and the shape operator of real hypersurfaces in CP^{2} and CH^{2}},
  author = {K. Panagiotidou},
  journal= {arXiv preprint arXiv:1209.0131},
  year   = {2012}
}

Comments

Includes basic relations from section 3 of arXiv:1201.2540 in order for the reader to fully understand methodology and results

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