On some explicit constructions of dually flat Finsler metrics
نویسندگان
چکیده
منابع مشابه
on a class of locally dually flat finsler metrics with isotropic s-curvature
dually flat finsler metrics form a special and valuable class of finsler metrics in finsler information geometry,which play a very important role in studying flat finsler information structure. in this paper, we prove that everylocally dually flat generalized randers metric with isotropic s-curvature is locally minkowskian.
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...
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متن کاملOn dually flat general $(\alpha,\beta)$-metrics
Based on the previous research, in this paper we study the dual flatness of a special class of Finsler metrics called general (α, β)-metrics, which is defined by a Riemannian metric α and a 1-form β. By using a new kind of deformation technique, we construct many non-trivial explicit dually flat general (α, β)-metrics.
متن کاملOn dually flat $(\alpha,\beta)$-metrics
The dual flatness for Riemannian metrics in information geometry has been extended to Finsler metrics. The aim of this paper is to study the dual flatness of the so-called (α, β)-metrics in Finsler geometry. By doing some special deformations, we will show that the dual flatness of an (α, β)-metric always arises from that of some Riemannian metric in dimensional n ≥ 3.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2013
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.04.028