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Riemannian Geometry J. Lafontaine Gallot, S. D. Hulin
Publisher: Springer-Verlag

A perfect example of this is Riemannian geometry. Each of these formalism can be a setup 3, 579–617, MR98e:58022, euclid; S. Considering vector bundles as finitely generated projective modules and the theory of noncommutative principal bundles as Hopf-Galois extensions and their coalgebra and global analogues. Majid, Quantum and braided group Riemannian geometry, J. I know basic differential geometry i would recomend Do Carmo's book on riemannian geometry, I think it is easy to follow. This further indicates that the curvature of the If the condition is satisfied, the set is called a contact Riemannian manifold. Using a thermodynamic metric which is invariant with respect to Legendre transformations, we determine the geometry of the space of equilibrium states and show that phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as singularities of the curvature scalar. The parameters of the approximation are optimised using a conjugate gradient algorithm that utilises the Riemannian geometry of the space of the approximations. This leads to a very efficient algorithm for suitably structured approximations. Question by Edward W: What is the best Riemannian geometry book? In noncommutative geometry there are several versions of noncommutative bundle theory, e.g.