{"title":"Statistical structures and Killing vector fields on tangent bundles with respect to two different metrics","authors":"Murat ALTUNBAŞ","doi":"10.31801/cfsuasmas.1160135","DOIUrl":null,"url":null,"abstract":"Let $(M,g)$ be a Riemannian manifold and $TM$ be its tangent bundle. The purpose of this paper is to study statistical structures on $TM$ with respect to the metrics $G_{1}=^{c}g+^{v}(fg)$ and $G_{2}=^{s}g_{f}+^{h}g,\\ $ where $f$ is a smooth function on $M,$ $^{c}g$ is the complete lift of $g$, $^{v}(fg)$ is the vertical lift of $fg$, $^{s}g_{f}$ is a metric obtained by rescaling the Sasaki metric by a smooth function $f$ and $^{h}g$ is the horizontal lift of $g.$ Moreover, we give some results about Killing vector fields on $TM$ with respect to these metrics.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31801/cfsuasmas.1160135","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let $(M,g)$ be a Riemannian manifold and $TM$ be its tangent bundle. The purpose of this paper is to study statistical structures on $TM$ with respect to the metrics $G_{1}=^{c}g+^{v}(fg)$ and $G_{2}=^{s}g_{f}+^{h}g,\ $ where $f$ is a smooth function on $M,$ $^{c}g$ is the complete lift of $g$, $^{v}(fg)$ is the vertical lift of $fg$, $^{s}g_{f}$ is a metric obtained by rescaling the Sasaki metric by a smooth function $f$ and $^{h}g$ is the horizontal lift of $g.$ Moreover, we give some results about Killing vector fields on $TM$ with respect to these metrics.