多重扭曲乘积浸入  

On Multiply Warped Product Immersion

作　　者：陈海莲[1] 钟定兴[2] CHEN Hailian;ZHONG Dingxing(College of Science and Technology,Gannan Normal University,Ganzhou 341000,China;School of Mathematics and Computer Science,Gannan Normal University,Ganzhou 341000,China)

机构地区：[1]赣南师范大学科技学院,江西赣州341000 [2]赣南师范大学数学与计算机科学学院,江西赣州341000

出　　处：《赣南师范大学学报》2022年第3期7-10,共4页Journal of Gannan Normal University

基　　金：国家自然科学基金(11361004);江西省基础教育研究课题(SZUGKSX2021-1000)。

摘　　要：扭曲乘积流形是乘积流形的自然推广.扭曲乘积流形与理论物理有密切联系,爱因斯坦场方程和规范场方程的某些解是扭曲乘积流形.文章研究多重扭曲乘积流形到多重扭曲乘积流形的等距浸入的有关性质,得到了这样的等距浸入为全测地浸入,或为全脐浸入,或为极小浸入的充要条件.The warded product manifolds is nature generalizations of the notion of Cartesian product manifolds.The warded product manifolds are closely related to the theoretical physics,many exact solutions of the Einstein field equations and modified field equations are warped manifolds.In this paper,we study the related properties of the isometric immersion of the multiply warped product manifolds into the multiply warded product manifolds,the necessary and sufficient conditions for such isometric immersion to be total geodesic immersion,total umbilical immersion or minimal immersion are obtained.

关 键 词：扭曲乘积流形 多重扭曲乘积浸入 全测地子流形 全脐子流形 极小子流形 

分 类 号：O186.12[理学—数学]