{"title":"CR STATISTICAL SUBMANIFOLDS","authors":"M. Milijević","doi":"10.2206/kyushujm.73.89","DOIUrl":null,"url":null,"abstract":"The non-existence of CR submanifolds of maximal CR dimension with umbilical shape operator in holomorphic statistical manifolds is proven. Our results are a generalization of the known results in the theory of CR submanifolds in complex space forms. Statistical manifolds in this paper are considered as manifolds consisting of certain probability density functions. In this setting we have two shape operators in the distinguished normal vector field direction with respect to the affine connection of the ambient space, and the one with respect to the dual connection. After obtaining the fundamental equations for CR submanifolds in holomorphic statistical manifolds, we examine umbilical dual shape operators.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyushu Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2206/kyushujm.73.89","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
The non-existence of CR submanifolds of maximal CR dimension with umbilical shape operator in holomorphic statistical manifolds is proven. Our results are a generalization of the known results in the theory of CR submanifolds in complex space forms. Statistical manifolds in this paper are considered as manifolds consisting of certain probability density functions. In this setting we have two shape operators in the distinguished normal vector field direction with respect to the affine connection of the ambient space, and the one with respect to the dual connection. After obtaining the fundamental equations for CR submanifolds in holomorphic statistical manifolds, we examine umbilical dual shape operators.
期刊介绍：
The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total.
More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.
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