Real hypersurfaces in complex projective space whose structure Jacobi operator is Lie \(\xi\)-parallel
type: Item
instance of: scholarly article
title: Real hypersurfaces in complex projective space whose structure Jacobi operator is Lie \(\xi\)-parallel
zbMATH Open document ID: 1108.53026
author: Juan D. Pérez
author: Florentino G. Santos
author: Young Jin Suh
published in: Differential Geometry and its Applications
publication date: 2005-05-04T00:00:00Z
review text: It is well-known that on any real hypersurface \(M\) of the complex projective space \(\mathbb CP^m\), an almost contact metric structure \((\varphi,\xi,\eta,g)\) is induced. In this paper, it is proved for \(M\) that if \(\mathcal L_{\xi}R_{\xi}=0\), where \(\mathcal L_{\xi}\) is the Lie derivative and \(R_{\xi}\) is the Jacobi operator corresponding to \(\xi\), then \(M\) is locally congruent to a tube of radius \(\pi/4\) over a complex submanifold, or to either a geodesic hypersphere or a tube over totally geodesic \(\mathbb CP^k\), \(0<k<m-1\), with radius \(r\not=\pi/4\). The paper should be compared to the previous one [Publ. Math. 66, No. 3--4, 269--282 (2005; Zbl 1081.53051)].
reviewed by: Zbigniew Olszak
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53B25
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 2165116
zbMATH Keywords: hypersurface
zbMATH Keywords: complex projective space
zbMATH Keywords: Jacobi operator
MaRDI profile type: Publication
full work available at URL: j.difgeo.2004.10.005
OpenAlex ID: W2161222239
Wikidata QID: Q115357994
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DOI: 10.1016/J.DIFGEO.2004.10.005
description: scientific article; zbMATH DE number 2165116