Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

Lixu Yan, Yanlin Li (), Lokman Bilen and Aydın Gezer
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Lixu Yan: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Lokman Bilen: Faculty of Science and Art, Department of Mathematics, Iğdır University, Iğdır 76100, Turkey
Aydın Gezer: Faculty of Science, Department of Mathematics, Ataturk University, Erzurum 25240, Turkey

Mathematics, 2024, vol. 12, issue 9, 1-18

Abstract: Let ( M , ∇ , g ) be a statistical manifold and T M be its tangent bundle endowed with a twisted Sasaki metric G . This paper serves two primary objectives. The first objective is to investigate the curvature properties of the tangent bundle T M . The second objective is to explore conformal vector fields and Ricci, Yamabe, and gradient Ricci–Yamabe solitons on the tangent bundle T M according to the twisted Sasaki metric G .

Keywords: conformal vector field; Ricci and Yamabe solitons; statistical manifold; twisted Sasaki metric; tangent bundle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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