Clifford Henry Taubes
- 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 ...
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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 the tangent bundle of a manifold M (TM), called a Riemannian metric.Less
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 the tangent bundle of a manifold M (TM), called a Riemannian metric.
Clifford Henry Taubes
- 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
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 explains how this is done then considers the distance minimizing paths. The discussions cover Riemannian metrics and distance; length minimizing curves; the existence of geodesics; examples of metrics with their corresponding geodesics; geodesics on SO(n); geodesics on U(n) and SU(n); and geodesics and matrix groups.Less
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 explains how this is done then considers the distance minimizing paths. The discussions cover Riemannian metrics and distance; length minimizing curves; the existence of geodesics; examples of metrics with their corresponding geodesics; geodesics on SO(n); geodesics on U(n) and SU(n); and geodesics and matrix groups.
