Locally conformally Hermitian-flat manifolds
type: Item
instance of: scholarly article
title: Locally conformally Hermitian-flat manifolds
zbMATH Open document ID: 0845.53049
DOI: 10.1007/BF00774566
author: Koji Matsuo
published in: Annals of Global Analysis and Geometry
publication date: 1996-09-11T00:00:00Z
review text: The Hermitian connection on a Hermitian manifold is a connection preserving the holomorphic sections. It coincides with the Levi-Civita connection on Kähler manifolds. The author considers locally conformally Hermitian flat manifolds, i.e. Hermitian manifolds which are locally conformally related to flat (in the Hermitian sense) manifolds. The main purpose of this paper is to derive necessary and sufficient conditions for a Hermitian manifold to be locally conformally Hermitian flat. These conditions are given in terms of a conformally invariant tensor \({\mathcal B}_0\) and scalar curvatures. The author also constructs a family of examples.
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 761177
zbMATH Keywords: conformal invariance
zbMATH Keywords: Hermitian connection
zbMATH Keywords: locally conformally Hermitian flat
reviewed by: Neda Bokan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 761177