Contact hypersurfaces of Kähler manifolds
type: Item
instance of: scholarly article
title: Contact hypersurfaces of Kähler manifolds
zbMATH Open document ID: 1053.53040
author: Ramesh Sharma
published in: Journal of Geometry
publication date: 2004-05-27T00:00:00Z
review text: The author classifies contact hypersurfaces \(M\) of Kähler manifolds \(\overline M\) with second fundamental form being a Codazzi tensor. In arbitrary Kähler manifolds, such an \(M\) is either Sasakian and totally umbilical or locally isometric (up to certain transformation) to the unit tangent bundle of a space of constant curvature \(\neq 1\). If \(\overline M\) is a Calabi-Yau manifold (that is, has Ricci-flat Kähler metric), then \(M\) is either Sasakian and umbilical with unit mean curvature, or flat of dimension 3, or locally isometric to \(\mathbb R^{n-1}\times S^n(4)\), \(n > 2\).
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 2067302
zbMATH Keywords: Kähler manifold
zbMATH Keywords: contact hypersurface
zbMATH Keywords: Codazzi tensor
reviewed by: Paweł Walczak
MaRDI profile type: Publication
full work available at URL: s00022-003-1625-y
OpenAlex ID: W1974706392
DOI: 10.1007/S00022-003-1625-Y
description: scientific article; zbMATH DE number 2067302