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

Source: [The structure Jacobi operator and the shape operator of real hypersurfaces in CP^{2} and CH^{2}](<https://www.sota2.com/research/paper/68fa4fdd1e209131ce966cd4>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:32:41.498Z

Authors: K.Panagiotidou

Published: 2012-09-01T20:31:11.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1209.0131>)

[PDF](<https://arxiv.org/pdf/1209.0131.pdf>)