Conformal Control Tools for Statistical Manifolds and for γ -Manifolds

Iulia-Elena Hirica, Cristina-Liliana Pripoae, Gabriel-Teodor Pripoae and Vasile Preda
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Iulia-Elena Hirica: Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
Cristina-Liliana Pripoae: Department of Applied Mathematics, The Bucharest University of Economic Studies, Piata Romana 6, RO-010374 Bucharest, Romania
Gabriel-Teodor Pripoae: Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania
Vasile Preda: Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, RO-010014 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 7, 1-15

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

Keywords: ?-manifolds; statistical manifolds; dual connections; conformal connections; Fisher metric; control tools; Weyl manifolds; f -conformal equivalence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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