The structure Jacobi operator and the shape operator of real hypersurfaces in \(\mathbb CP^2\) and \(\mathbb CH^2\)
type: Item
instance of: scholarly article
title: The structure Jacobi operator and the shape operator of real hypersurfaces in \(\mathbb CP^2\) and \(\mathbb CH^2\)
zbMATH Open document ID: 1305.53058
author: Konstantina Panagiotidou
published in: Beiträge zur Algebra und Geometrie
publication date: 2014-10-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/1209.0131
review text: Let \((M, g)\) be a real hypersurface in \(\mathbb{C}P^2\) or \(\mathbb{C}H^2\) and \(A\) its shape operator. \(M\) carries a natural vector field \(\xi \) induced by a fixed unit normal vector field and the Kählerian structure of the ambient manifold; hence we have on \(M\) the structure Jacobi operator \(l=R(\cdot , \xi )\xi \). The two main results of the paper prove that there does not exist \((M, g)\) satisfying \(\mathcal{L}_Xl=\nabla _Xl\) respectively \(\mathcal{L}_XA=\nabla _XA\) for all \(X\in \mathbb{D}\) where \(\mathbb{D}\) is the distribution \(g\)-orthogonal to \(\xi \).
reviewed by: Constantin Călin
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53D15
zbMATH DE Number: 6362514
zbMATH Keywords: real hypersurface
zbMATH Keywords: structure Jacobi operator
zbMATH Keywords: shape operator
zbMATH Keywords: Lie derivative
zbMATH Keywords: complex projective space
zbMATH Keywords: complex hyperbolic space
MaRDI profile type: Publication
OpenAlex ID: W185790566
arXiv ID: 1209.0131
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DOI: 10.1007/S13366-013-0174-2
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description: scientific article; zbMATH DE number 6362514