Connections on Manifolds: A Modern Approach to Classical Differential Geometry

Author

Jed Allen Wilshire, The University of Texas Rio Grande Valley

Date of Award

12-1-2025

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Sergey Grigorain

Second Advisor

Alexey Garber

Third Advisor

Alexey Glazyrin

Abstract

The purpose of this thesis is to connect modern differential geometry concepts to the classical differential geometry study of surfaces, specifically spheres. This thesis will cover the topics of Riemannian manifolds, tangent spaces, vectors, vector fields, the connection of Levi-Civita, the Christoffel symbols, and Riemannian curvature. Each concept will be demonstrated on the well known unit sphere manifold.

Comments

Copyright 2025 Jed Allen Wilshire. All Rights Reserved. https://proquest.com/docview/3292437292

Recommended Citation

Wilshire, J. A. (2025). Connections on Manifolds: A Modern Approach to Classical Differential Geometry [Master's thesis, The University of Texas Rio Grande Valley]. ScholarWorks @ UTRGV. https://scholarworks.utrgv.edu/etd/1835