Submersions of CR submanifolds
type: Item
instance of: scholarly article
title: Submersions of CR submanifolds
zbMATH Open document ID: 0619.58004
author: Shoshichi Kobayashi
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1987-01-01T00:00:00Z
review text: A real submanifold N of a complex Banach manifold V is called a CR submanifold if \(T^ h=TN\cap J(TN)\) is a complex subbundle of the tangent bundle TV; J being the relevant complex structure. Assume V Kähler, let \(T^{\vee}N\) be the orthogonal complement of \(T^ hN\) in TN, \(T^ nN\) be the normal bundle. Assume that J interchanges \(T^{\vee}N\) and \(T^ nN\). Let \(\pi\) : \(N\to W\) be a submersion on an almost Hermitian manifold W such that \(T^{\vee}N\) is a kernel of \(\pi\) and \(\pi\) induces a complex isometry of \(T^ hN\) and TW. Under these assumptions, W is Kähler and \(H^ V=H^ W-4| B|^ 2\), where \(H^ V\) \((H^ W)\) is the holomorphic sectional curvature and B is the second fundamental form of N. As an application, the moduli space of stable holomorphic vector bundles over compact Riemann surfaces has nonnegative holomorphic sectional curvature.
Mathematics Subject Classification ID: 58B20
Mathematics Subject Classification ID: 32L05
Mathematics Subject Classification ID: 53B35
zbMATH DE Number: 4005174
zbMATH Keywords: Kaehler manifold
zbMATH Keywords: Riemannian submersion
zbMATH Keywords: Banach manifold
zbMATH Keywords: sectional curvature
zbMATH Keywords: holomorphic vector bundles
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228282
OpenAlex ID: W1992432286
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DOI: 10.2748/TMJ/1178228282
description: scientific article; zbMATH DE number 4005174