Differential Forms and Applications

Differential Forms and Applications

Author: Manfredo P. Do Carmo

Publisher: Springer Science & Business Media

ISBN: 9783642579516

Category: Mathematics

Page: 118

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An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.
Differential Forms and Applications
Language: en
Pages: 118
Authors: Manfredo P. Do Carmo
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the
Visual Differential Geometry and Forms
Language: en
Pages: 584
Authors: Tristan Needham
Categories: Mathematics
Type: BOOK - Published: 2021-07-13 - Publisher: Princeton University Press

An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical
The Pullback Equation for Differential Forms
Language: en
Pages: 436
Authors: Gyula Csató, Bernard Dacorogna, Olivier Kneuss
Categories: Mathematics
Type: BOOK - Published: 2011-11-12 - Publisher: Springer Science & Business Media

An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem is therefore to find a map φ so that it satisfies the pullback equation: φ*(g) = f. In more physical terms, the question under consideration
Geometric Methods and Applications
Language: en
Pages: 566
Authors: Jean Gallier
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric
Differential Geometry: Theory and Applications
Language: en
Pages:
Authors: Jean Gallier
Categories: Mathematics
Type: BOOK - Published: - Publisher:

Books about Differential Geometry: Theory and Applications