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UBC Theses and Dissertations
Connections Nicolson, Robert Alexander
Abstract
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.
Item Metadata
Title |
Connections
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1972
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Description |
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.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-04-13
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Provider |
Vancouver : University of British Columbia Library
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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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DOI |
10.14288/1.0080458
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
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.