Book by JG Vargas: Differential Geometry for Physicists and Mathematicians


Differential Geometry for Physicists and Mathematicians: Moving Frames and Differential Forms: From Euclid Past Riemann

by Jose G. Vargas

Description:

This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative — almost like a story being told — that does not impede sophistication and deep results.

It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas of mathematics that are of interest to physicists and mathematicians, but are largely overlooked. Among these is Clifford Algebra and its uses in conjunction with differential forms and moving frames. It opens new research vistas that expand the subject matter.

In an appendix on the classical theory of curves and surfaces, the author slashes not only the main proofs of the traditional approach, which uses vector calculus, but even existing treatments that also use differential forms for the same purpose.

Readership: Physicists and mathematicians working on differential geometry.

Contents (http://www.worldscientific.com/worldscibooks/10.1142/8888):

  • Introduction:
    • Orientations
  • Tools:
    • Differential Forms
    • Vector Spaces and Tensor Products
    • Exterior Differentiation
  • Two Klein Geometries:
    • Affine Klein Geometry
    • Euclidean Klein Geometry
  • Cartan Connections:
    • Generalized Geometry Made Simple
    • Affine Connections
    • Euclidean Connections
    • Riemannian Spaces and Pseudo-Spaces
  • The Future?:
    • Extensions of Cartan
    • Understand the Past to Imagine the Future
    • A Book of Farewells

Source: Email from J.G. Vargas, 22 Apr. 2014, josegvargas_AT_earthlink.net, http://www.amazon.com/Differential-Geometry-Physicists-Mathematicians-Riemann/dp/981456639X/ref=sr_1_1?s=books&ie=UTF8&qid=1398325103&sr=1-1&keywords=Differential+Geometry+for+Physicists+and+Mathematicians, http://www.worldscientific.com/worldscibooks/10.1142/8888, http://www.worldscientific.com/worldscibooks/10.1142/8888#t=toc

1 Comment

Filed under publications

One response to “Book by JG Vargas: Differential Geometry for Physicists and Mathematicians

  1. Pingback: Book discount for J.G. Vargas: Differential Geometry for Physicists and Mathematicians | GA Net Updates

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s