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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

5 votes

Reading list for basic differential geometry?

I would like to suggest the three volume set by Dubrovin, Fomenko, Novikov (Modern Geometry--Methods and Applications) as a supplementary reference. They have a somewhat unique style and approach to t …
4 votes

Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature

In section 4.5 of his big book on Riemannian geometry, Berger has a discussion on the question of to what degree (and in what sense) the curvature determines the metric. He quotes the following theor …
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