UM Salama¹*, Ahmed ABD Alla A Elemam²

¹Department of Mathematics, Faculty of Addayer College University, Saudi Arabia ²Department of Mathematics, Faculty of Education Jazan University, Saudi Arabia

*Corresponding Author: UM Salama, Department of Mathematics, Faculty of Addayer College University, Saudi Arabia.

Received: December 21, 2023; Published: December 29, 2023

Abstract

In this study, we introduce a manifold which help to give further understanding of spaces and applied features of spaces. we have introduced Riemannian Manifold, Lie groups. In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of -dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not self-crossing curve. concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions.

Keywords: The Rn Space; Euclidean Space; Homeomorphism; Housdorff Space; Metric Spaces; Topological Manifold Differentiable Manifolds; Sub Manifolds; Riemannian Manifold; Vector Field; Lie Groups

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Citation

Citation: UM Salama., et al. “Manifolds and Lie groups". Acta Scientific Computer Sciences 6.1 (2024): 29-39.

Copyright

Copyright: © 2024 UM Salama., et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.