Some remarks on Einstein-Randers metrics
نویسندگان
چکیده
In this essay, we study the sufficient and necessary conditions for a Randers metrc to be of constant Ricci curvature, without the restriction of strong convexity (regularity). A classification result for the case ‖β‖α > 1 is provided, which is similar to the famous Bao-Robles-Shen’s result for strongly convex Randers metrics (‖β‖α < 1). Based on some famous vacuum Einstein metrics in General Relativity, many non-regular Einstein-Randers metrics are constructed. Besides, we find that the case ‖β‖α ≡ 1 is very distinctive. These metrics will be called singular Randers metrics or parabolic Finsler metrics since their indicatrixs are parabolic hypersurfaces. A preliminary discussion for such metrics is provided.
منابع مشابه
On 5-dimensional 2-step homogeneous randers nilmanifolds of Douglas type
In this paper we first obtain the non-Riemannian Randers metrics of Douglas type on two-step homogeneous nilmanifolds of dimension five. Then we explicitly give the flag curvature formulae and the $S$-curvature formulae for the Randers metrics of Douglas type on these spaces. Moreover, we prove that the only simply connected five-dimensional two-step homogeneous Randers nilmanifolds of D...
متن کاملOn Randers metrics of reversible projective Ricci curvature
projective Ricci curvature. Then we characterize isotropic projective Ricci curvature of Randers metrics. we also show that Randers metrics are PRic-reversible if and only if they are PRic-quadratic../files/site1/files/0Abstract2.pdf
متن کاملOn dually flat Randers metrics
The notion of dually flat Finsler metrics arise from information geometry. In this paper, we will study a special class of Finsler metrics called Randers metrics to be dually flat. A simple characterization is provided and some non-trivial explicit examples are constructed. In particular, We will show that the dual flatness of a Randers metric always arises from that of some Riemannian metric b...
متن کاملThe Index of a Geodesic in a Randers Space and Some Remarks about the Lack of Regularity of the Energy Functional of a Finsler Metric
In a series of papers ([2, 3, 4]) the relations existing between the metric properties of Randers spaces and the conformal geometry of stationary Lorentzian manifolds were discovered and investigated. These relations were called in [4] Stationary-to-Randers Correspondence (SRC). In this paper we focus on one aspect of SRC, the equality between the index of a geodesic in a Randers space and that...
متن کاملRanders Metrics of Scalar Flag Curvature
We study an important class of Finsler metrics — Randers metrics. We classify Randers metrics of scalar flag curvature whose S-curvatures are isotropic. This class of Randers metrics contains all projectively flat Randers metrics with isotropic S-curvature and Randers metrics of constant flag curvature.
متن کامل