On Randers metrics with isotropic S-curvature

“…Randers metrics of constant flag curvature (or quadratic Riemann curvature) have constant S-curvature [3,10]. In terms of the navigation representation, they are produced from Riemannian metrics and homothetic vector fields [13,16,22,23]. In fact, C. Robles classified geodesics in Randers manifolds of constant flag curvature [17].…”

Section: Introductionmentioning

confidence: 99%

On geodesics of Finsler metrics via navigation problem

Huang

2011

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. This paper is devoted to a study of geodesics of Finsler metrics via Zermelo navigation. We give a geometric description of the geodesics of the Finsler metric produced from any Finsler metric and any homothetic field in terms of navigation representation, generalizing a result previously only known in the case of Randers metrics with constant S-curvature. As its application, we present explicitly the geodesics of the Funk metric on a strongly convex domain.

show abstract

“…The notion of S-curvature is originally introduced by Shen for the volume comparison theorem which interacts with other Riemannian and non-Riemannian curvatures [14,18,19]. The Finsler metric F is said to be of isotropic S-curvature if S = (n + 1)cF , where c = c(x) is a scalar function on M .…”

Section: Introductionmentioning

confidence: 99%

On generalized Douglas–Weyl (α, β)-metrics

Tayebi

Sadeghi

2015

Acta. Math. Sin.-English Ser.

View full text Add to dashboard Cite

In this paper, we study generalized Douglas-Weyl (α, β)-metrics. Suppose that a regular (α, β)-metric F is not of Randers type. We prove that F is a generalized Douglas-Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover, by ignoring the regularity, if F is not a Berwald metric, then we find a family of almost regular Finsler metrics which is not Douglas nor Weyl. As its application, we show that generalized Douglas-Weyl square metric or Matsumoto metric with isotropic mean Berwald curvature are Berwald metrics.

show abstract

On Randers metrics with isotropic S-curvature

Cited by 60 publications

References 12 publications

Randers Metrics of Scalar Flag Curvature

Randers Metrics of Scalar Flag Curvature

On geodesics of Finsler metrics via navigation problem

On generalized Douglas–Weyl (α, β)-metrics

Contact Info

Product

Resources

About