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Metrics on vector bundles

Clifford Henry Taubes

in Differential Geometry: Bundles, Connections, Metrics and Curvature

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.003.0007
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

This chapter discusses the following: metrics and transition functions for real vector bundles; metrics and transition functions for complex vector bundles; metrics, algebra and maps; and a metric on ... More


Geodesics

Clifford Henry Taubes

in Differential Geometry: Bundles, Connections, Metrics and Curvature

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.003.0008
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

Let M denote a smooth manifold. A metric on TM can be used to define a notion of the distance between any two points in M and the distance travelled along any given path in M. This chapter first ... More


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