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Differential GeometryBundles, Connections, Metrics and Curvature$
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Clifford Henry Taubes

Print publication date: 2011

Print ISBN-13: 9780199605880

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199605880.001.0001

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Vector bundles with ℂn as fiber

Vector bundles with ℂn as fiber

(p.59) 6 Vector bundles with ℂn as fiber
Differential Geometry

Clifford Henry Taubes

Oxford University Press

Just as there are vector spaces over ℂ, there are vector bundles whose fibres can be consistently viewed as ℂn for some n. This chapter first defines these objects and then provides number of examples. The discussions cover complex vector bundles; complex bundles over surfaces in ℝ3; the tangent bundle to a surface in ℝ3; bundles over 4-dimensional submanifolds in ℝ5; complex bundles over 4-dimensional manifolds; complex Grassmannians; the exterior product construction; algebraic operations; and pull-back.

Keywords:   vector spaces, vector bundles, fibres, complex bundles, tangent bundle, manifolds, Grassmannians, pull-back

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