%0 Journal Article
%T 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
%A Zhiwei Yan
%J Advances in Pure Mathematics
%P 207-210
%@ 2160-0384
%D 2023
%I Scientific Research Publishing
%R 10.4236/apm.2023.135014
%X 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 TpM for all p กส S, which depends smoothly on p กส S. The purpose of this article is to figure out that the fibre metric on TM|s can always be extended to a Riemannian metric on TM from a special perspective.
%K Embedded Smooth Manifold
%K Superplane
%K Riemannian Metric
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=124834