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

22 votes
5 answers
5k views

On the generalized Gauss-Bonnet theorem

I am trying to learn about basic characteristic classes and Generalized Gauss-Bonnet Theorem, and my main reference at the moment is From calculus to cohomology by Madsen & Tornehave. I know the state …
7 votes
1 answer
826 views

Curvature and Riemannian metric

Hi all, I am going to give a talk in a seminar about the general theme 'sum of squares'. My interests lie in Differential Geometry, so I recalled that the curvature is a local invariant, an obstructi …
6 votes
2 answers
4k views

Killing vectors and Ricci Tensor

Hi all, We all know that the lie derivative of the metric tensor along a Killing Vector vanishes, by definition. I am trying to show that the Lie derivative of the Ricci tensor along a Killing vector …