A Discussion on the Establishment That a Fibre Metric on the Positive Definite Real Inner-Product of a Properly Embedded Smooth Submanifold Be Always Extended to a Riemannian Metric on the Positive Definite Real Inner-Product  

作　　者：Zhiwei Yan Zhiwei Yan(Department of Mathmetics, Jimei University, Xiamen, China)

机构地区：[1]Department of Mathmetics, Jimei University, Xiamen, China

出　　处：《Advances in Pure Mathematics》2023年第5期207-210,共4页理论数学进展（英文）

摘　　要：Let M be a smooth manifold and S ⊆ M a properly embedded smooth submanifold. Suppose that we have a fibre metric on TM|_s i.e. a positive definite real inner-product on T_pM for all p ∈ S, which depends smoothly on p ∈ S. The purpose of this article is to figure out that the fibre metric on TM|s</sub> can always be extended to a Riemannian metric on TM from a special perspective.Let M be a smooth manifold and S ⊆ M a properly embedded smooth submanifold. Suppose that we have a fibre metric on TM|_s i.e. a positive definite real inner-product on T_pM for all p ∈ S, which depends smoothly on p ∈ S. The purpose of this article is to figure out that the fibre metric on TM|s</sub> can always be extended to a Riemannian metric on TM from a special perspective.

关 键 词：Embedded Smooth Manifold Superplane Riemannian Metric 

分 类 号：O18[理学—数学]