Cr统计子流形

IF 0.6 4区 数学 Q3 MATHEMATICS
M. Milijević
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引用次数: 4

摘要

证明了全纯统计流形中具有脐形算子的CR子流形的不存在性。我们的结果是对复空间形式CR子流形理论中已知结果的推广。本文认为统计流形是由一定的概率密度函数组成的流形。在这种情况下,我们有两个形状算符在区分法向量场方向上关于周围空间的仿射连接,一个关于对偶连接。在得到全纯统计流形中CR子流形的基本方程后,研究了脐对偶形状算子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
CR STATISTICAL SUBMANIFOLDS
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.
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来源期刊
CiteScore
0.80
自引率
0.00%
发文量
10
审稿时长
>12 weeks
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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