The main purpose of this exposition is to explore the relations between the notions of covariant derivative,
connection, and spray.
We begin by introducing the basic definitions and then use a method of Gromoll, Klingenberg and Meyer to show that covariant derivatives and connections on vector bundles are in a natural one-to-one correspondence.
We conclude by showing that on the tangent bundle of a manifold, sprays and "symmetric" connections are in a natural one-to-one correspondence. Although we use a different method, this re-establishes a result of Ambrose, Palais, and Singer. / Science, Faculty of / Mathematics, Department of / Graduate
Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/33610 |
Date | January 1972 |
Creators | Nicolson, Robert Alexander |
Publisher | University of British Columbia |
Source Sets | University of British Columbia |
Language | English |
Detected Language | English |
Type | Text, Thesis/Dissertation |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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