The Australian Journal of Mathematical Analysis and Applications

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Paper's Title:

Global Analysis on Riemannian Manifolds


Louis Omenyi and Michael Uchenna

Department of Mathematics, Computer Science, Statistics and Informatics,
Alex Ekwueme Federal University, Ndufu-Alike,


In this paper, an exposition of the central concept of global analysis on a Riemannan manifold is given. We extend the theory of smooth vector fields from open subsets of Euclidean space to Riemannan manifolds. Specifically, we prove that a Riemannian manifold admits a unique solution for a system of ordinary differential equations generated by the flow of smooth tangent vectors. The idea of partial differential equations on Riemannian manifold is highlighted on the unit sphere.

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