Conformal Control Tools for Statistical Manifolds and for γ-Manifolds

被引：2

作者：

Hirica, Iulia-Elena ^{[1
]}

Pripoae, Cristina-Liliana ^{[2
]}

Pripoae, Gabriel-Teodor ^{[1
]}

Preda, Vasile ^{[1
,3
,4
]}

机构：

[1] Univ Bucharest, Fac Math & Comp Sci, Acad 14, RO-010014 Bucharest, Romania

[2] Bucharest Univ Econ Studies, Dept Appl Math, Piata Romana 6, RO-010374 Bucharest, Romania

[3] Romanian Acad, Gheorghe Mihoc Caius Iacob Inst Math Stat & Appl, 2 Calea 13 Septembrie,13,Sect 5, RO-050711 Bucharest, Romania

[4] Romanian Acad, Costin C Kiritescu Natl Inst Econ Res, 3 Calea 13 Septembrie,13,Sect 5, RO-050711 Bucharest, Romania

来源：

MATHEMATICS | 2022年 / 10卷 / 07期

关键词：

gamma-manifolds; statistical manifolds; dual connections; conformal connections; Fisher metric; control tools; Weyl manifolds; f-conformal equivalence; GEOMETRY;

D O I：

10.3390/math10071061

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The theory of statistical manifolds w.r.t. a conformal structure is reviewed in a creative manner and developed. By analogy, the gamma-manifolds are introduced. New conformal invariant tools are defined. A necessary condition for the f-conformal equivalence of gamma-manifolds is found, extending that for the alpha-conformal equivalence for statistical manifolds. Certain examples of these new defined geometrical objects are given in the theory of Iinformation.

引用

页数：15

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