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Randers Metrics of Constant Scalar Curvature

  Published:2011-08-30
 Printed: Sep 2013
  • Esra Sengelen Sevim,
    Department of Mathematics, Istanbul Bilgi University, 34440, Kurtulusderesi Cad. No: 48 Dolapdere/Beyoglu, Istanbul, Turkey
  • Zhongmin Shen,
    Department of Mathematical Sciences, Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, IN 46202-3216, USA
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Abstract

Randers metrics are a special class of Finsler metrics. Every Randers metric can be expressed in terms of a Riemannian metric and a vector field via Zermelo navigation. In this paper, we show that a Randers metric has constant scalar curvature if the Riemannian metric has constant scalar curvature and the vector field is homothetic.
Keywords: Randers metrics, scalar curvature, S-curvature Randers metrics, scalar curvature, S-curvature
MSC Classifications: 53C60, 53B40 show english descriptions Finsler spaces and generalizations (areal metrics) [See also 58B20]
Finsler spaces and generalizations (areal metrics)
53C60 - Finsler spaces and generalizations (areal metrics) [See also 58B20]
53B40 - Finsler spaces and generalizations (areal metrics)
 

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