On Kropina metrics of scalar flag curvature
نویسندگان
چکیده
منابع مشابه
Randers 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 کاملOn conformal transformation of special curvature of Kropina metrics
An important class of Finsler metric is named Kropina metrics which is defined by Riemannian metric α and 1-form β which have many applications in physic, magnetic field and dynamic systems. In this paper, conformal transformations of χ-curvature and H-curvature of Kropina metrics are studied and the conditions that preserve this quantities are investigated. Also it is shown that in the ...
متن کاملClassification of Randers Metrics of Scalar Flag Curvature
This is a survey article about the recent developments in classifying Randers metrics of scalar flag curvature under an additional condition on the isotropic S-curvature. The authors give an outline of the proof for the classification theorem.
متن کاملFinsler metrics of scalar flag curvature and projective invariants
In this paper, we define a new projective invariant and call it W̃ -curvature. We prove that a Finsler manifold with dimension n ≥ 3 is of constant flag curvature if and only if its W̃ -curvature vanishes. Various kinds of projectively flatness of Finsler metrics and their equivalency on Riemannian metrics are also studied. M.S.C. 2010: 53B40, 53C60.
متن کاملRanders Metrics of Sectional Flag Curvature
A Finsler metric is of sectional flag curvature if its flag curvature depends only on the section. In this article, we characterize Randers metrics of sectional flag curvature. It is proved that any non-Riemannian Randers metric of sectional flag curvature must have constant flag curvature if the dimension is greater than two. 0. Introduction Finsler geometry has a long history dated from B. Ri...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2013
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2013.03.001