Acta Mathematica Sinica, English Series

, Volume 31, Issue 5, pp 879–892 | Cite as

On conformally flat (α, β)-metrics with special curvature properties

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Abstract

In this paper, we study a significant non-Riemannian quantity Ξ-curvature, which is defined by S-curvature. Firstly, we obtain the formula of Ξ-curvature for (α, β)-metrics. Based on it, we show that the Ξ-curvature vanishes for a class of (α, β)-metrics. In the end, we get the relation of Ξ-curvature for conformally related Finsler metrics, and classify conformally flat (α, β)-metrics with almost vanishing Ξ-curvature.

Keywords

(α, β)-metrics conformally flat Ξ-curvature 

MR(2010) Subject Classification

53B40 53C60 
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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIndiana University Purdue University IndianapolisIndianapolisUSA
  2. 2.School of Mathematics and StatisticsChongqing University of TechnologyChongqingP. R. China

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