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A comprehensive introduction to differential geometry

Author: Michael Spivak
Publisher: Berkeley : Publish or Perish, Inc., 1979.
Edition/Format:   Print book : English : 2d edView all editions and formats
Database:WorldCat
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Additional Physical Format: Online version:
Spivak, Michael.
Comprehensive introduction to differential geometry.
Berkeley : Publish or Perish, inc., 1979
(OCoLC)622233942
Document Type: Book
All Authors / Contributors: Michael Spivak
ISBN: 0914098837 9780914098836 0914098799 9780914098799 0914098845 9780914098843 0914098888 9780914098881 0914098829 9780914098829
OCLC Number: 5045694
Description: 5 volumes : illustrations ; 24 cm
Contents: vol. I. Manifolds --
Differentiable structures --
The tangent bundle --
Tensors --
Vector fields and differential equations --
Integral manifolds --
Differential forms --
Integration --
Riemannian metrics --
Lie groups --
Excursion in the realm of algebraic topology --
vol. II. Curves in the plane and in space --
What they knew about surfaces before Gauss --
The curvature of surfaces in space --
The curvature of higher dimensional manifolds --
The absolute differential calculus (The Ricci calculus); or, the Debauch of indices --
The [nabla / del] operator --
The Repère mobile (The moving frame) --
Connections in principal bundles --
vol. III. The fundamental equations for hypersurfaces --
Elements of the theory of surfaces in IR³ --
A compendium of surfaces --
Curves on surfaces --
Complete surfaces of constant curvature --
The Gauss-Bonnet theorem and related topics --
vol. IV. Higher dimensions and codimensions --
The second variation --
Variations of lenght, area, and volume --
vol. V. And now a brief message from our sponsor --
Existence and non-existence of isometric imbeddings --
Rigidity --
The generalized Gauss-Bonnet theorem and what it means for mankind.
Other Titles: Differential geometry
Responsibility: Michael Spivak.

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