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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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Smooth manifolds

Smooth manifolds

Chapter:
(p.1) 1 Smooth manifolds
Source:
Differential Geometry
Author(s):

Clifford Henry Taubes

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199605880.003.0001

This chapter examines smooth manifolds. It first outlines the two theorems that govern various constructions of smooth manifolds: the inverse function theorem and the implicit function theorem. It then discusses submanifolds of ℝm; submanifolds of manifolds; ways to obtain new manifolds from old ones; and the Grassmannians.

Keywords:   inverse function theorem, implicit function theorem, submanifolds, Grassmannians

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