## Is there similar equation as in the Gauss-Bonnet theorem with respect to cocurvature? [closed]

Is there similar equation as in the Gauss-Bonnet theorem with respect to cocurvature?

Thanks

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What's cocurvature? – Deane Yang Nov 7 at 11:37
As a general rule, if you want to get a reasonable answer to your question, you should provide some background, explain why you are interested in the question, what you tried to resolve it yourself, etc., see MO FAQ. – Misha Nov 7 at 12:07
Google search for "cocurvature" revealed only a confused wikipedia article (seemingly written by a physicist, who is confusing tangent bundle of the base manifold $M$ and that of the associated principal $O(n)$-bundle over $M$) and nothing else of value. Judging by wikipedia article, it seems that cocurvature does not determine a tensor on the base $M$. What "Gauss-Bonnet" can possibly mean in this context is very much unclear. Voting to close. – Misha Nov 7 at 13:19