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

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. In noncommutative geometry there are several versions of noncommutative bundle theory, e.g. What (Extremely Basic) Riemannian Geometry really is. The familiar real line… http://upload.wikimedia.org/wikipedia/commons/d/d7/Real_number_line.svg. A rambling narrative of one man's journey through mathematics. Majid, Quantum and braided group Riemannian geometry, J. Mon, 23 Apr 2012 02:56:24 +0000. This is the paper: citeseerx.ist.psu.edu/viewdoc/… I didn't post it because almost none of it is relevant to the question. 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. Each of these formalism can be a setup 3, 579–617, MR98e:58022, euclid; S. I'm sorry if my question is not clear – I am just getting into these Riemannian geometry ideas. This further indicates that the curvature of the If the condition is satisfied, the set is called a contact Riemannian manifold.