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Domain of definition of a certain mapping

Suppose we have a compact smooth riemannian manifold $(M,g)$ and a $\mathcal{C}^2$ diffeomorphism $f$ of this manifold. I am studying the mapping $$\tilde{f}(x)= \exp_{f(x)}^{-1} \circ f \circ \exp_x \...
Giuseppe Tenaglia's user avatar