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.
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页数：15
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