Sep 28

Hamiltonian Reduction by Stages (Lecture Notes in

Format: Paperback

Language: English

Format: PDF / Kindle / ePub

Size: 7.54 MB

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This course introduces the mathematical areas of differential geometry and topology and how they are interrelated, and in particular studies various aspects of the differential geometry of surfaces. This is the beauty of topology, but it is not something that solving the equations of GR tells us. Addition of vectors and multiplication by scalars, vector spaces over R, linear combinations, linear independence, basis, dimension, linear and affine linear subspaces, tangent space at a point, tangent bundle; dot product, length of vectors, the standard metric on Rn; balls, open subsets, the standard topology on Rn, continuous maps and homeomorphisms; simple arcs and parameterized continuous curves, reparameterization, length of curves, integral formula for differentiable curves, parameterization by arc length.

Pages: 524

Publisher: Springer; 2007 edition (June 29, 2007)

ISBN: 3540724699

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