Some results on strong Randers metrics
type: Item
instance of: scholarly article
title: Some results on strong Randers metrics
zbMATH Open document ID: 1363.53066
author: Xiaohuan Mo
author: Hongmei Zhu
published in: Periodica Mathematica Hungarica
publication date: 2016-11-25T00:00:00Z
review text: The authors consider a strong Randers metric \(F=\alpha+| \beta| \) on a complex manifold. They prove that \(F\) is Kähler if and only if \(\beta\) is parallel with respect to \(\alpha\). Moreover, it is shown that if \(\alpha\) has constant holomorphic sectional curvature, it is shown that either \(F\) is usually Kählerian (i.e., \(F=\alpha\)), or it is Minkowskian of the form \(F=| v| ^2+\langle c,{\bar v}\rangle\), where \(c\) is constant vector and \(| v| =\sqrt{\langle v,v\rangle}\).
reviewed by: Vladimir Balan
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 53B40
zbMATH DE Number: 6656695
zbMATH Keywords: complex Finsler manifold
zbMATH Keywords: Kähler Randers metric
zbMATH Keywords: holomorphic sectional curvature
MaRDI profile type: Publication
full work available at URL: s10998-014-0082-8
OpenAlex ID: W2072354921
cites work: Finsler metrics - a global approach. With applications to geometric function theory
cites work: Kähler Finsler Manifolds of Constant Holomorphic Curvature
cites work: Q5263088
cites work: ON COMPLEX FINSLER SPACES WITH RANDERS METRIC
cites work: Zermelo navigation on Riemannian manifolds
cites work: Finsler geometry of projectivized vector bundles
cites work: Kähler Finsler metrics are actually strongly Kähler
cites work: ON COMPLEX RANDERS METRICS
cites work: Q2900171
cites work: An obstruction to the existence of Einstein Kaehler metrics
cites work: A vanishing theorem on Kähler Finsler manifolds
cites work: ON CHARACTERIZATIONS OF RANDERS NORMS IN A MINKOWSKI SPACE
cites work: Kähler-Einstein metrics with positive scalar curvature
cites work: On weighted complex Randers metrics
cites work: Bochner technique on strong Kähler-Finsler manifolds
cites work: On real and complex Berwald connections associated to strongly convex weakly Kähler-Finsler metric
cites work: Hodge decomposition theorem on strongly Kähler Finsler manifolds
DOI: 10.1007/S10998-014-0082-8
description: scientific article; zbMATH DE number 6656695