Real hypersurfaces which are contact in a nonflat complex space form
type: Item
instance of: scholarly article
title: Real hypersurfaces which are contact in a nonflat complex space form
zbMATH Open document ID: 1232.53045
author: Toshiaki Adachi
author: Masumi Kameda
author: Sadahiro Maeda
published in: Hokkaido Mathematical Journal
publication date: 2011-07-22T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.hokmj/1310042828
review text: Let \(\widetilde{M^n}(c)\), \(n \geq 2\), be a complex \(n\)-dimensional complete and simply connected Kähler manifold of constant holomorphic sectional curvature \(c \neq 0.\) As is well-known, every real hypersurface \(M^{2n-1}\) of \(\widetilde{M^n}(c)\) admits an almost contact metric structure \((\phi, \xi,\nu, g)\) induced from this ambient space. The authors investigate real hypersurfaces in \(\widetilde{M^n}(c)\) whose induced structure \((\phi, \xi,\nu, g)\) is a contact metric structure linking in this way submanifold theory and contact geometry and show nice examples of contact manifolds from the viewpoint of submanifold theory. They show that every real hypersurface which is contact in \(\widetilde{M^n}(c)\) is an orbit of some subgroup of the isometry group \(I(\widetilde{M^n}(c))\) of the ambient space \(\widetilde{M^n}(c).\)
reviewed by: Péter Olajos
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53D10
zbMATH DE Number: 5931182
zbMATH Keywords: nonflat complex spaces forms
zbMATH Keywords: real hyersurfaces
zbMATH Keywords: totally \(\nu\)-umbilic hypersurfaces
zbMATH Keywords: standard real hypersurfaces
zbMATH Keywords: homogeneous real hypersurfaces of type (B)
zbMATH Keywords: almost contact metric structure
zbMATH Keywords: Sasakian manifolds
zbMATH Keywords: Sasakian space forms
MaRDI profile type: Publication
OpenAlex ID: W1963482000
DOI: 10.14492/HOKMJ/1310042828
description: scientific article; zbMATH DE number 5931182