Dually Flat Fourth Root Metric
نویسندگان
چکیده
منابع مشابه
Characterization of locally dually flat first approximate Matsumoto metric
The concept of locally dually flat Finsler metrics originate from information geometry. As we know, (α, β)-metrics defined by a Riemannian metric α and an 1-form β, represent an important class of Finsler metrics, which contains the Matsumoto metric. In this paper, we study and characterize locally dually flat first approximation of the Matsumoto metric with isotropic S-curvature, which is not ...
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 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.
متن کاملMonte Carlo Information Geometry: The dually flat case
Exponential families and mixture families are parametric probability models that can be geometrically studied as smooth statistical manifolds with respect to any statistical divergence like the KullbackLeibler (KL) divergence or the Hellinger divergence. When equipping a statistical manifold with the KL divergence, the induced manifold structure is dually flat, and the KL divergence between dis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pure Mathematics
سال: 2013
ISSN: 2160-7583,2160-7605
DOI: 10.12677/pm.2013.33029