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Given a real analytic Riemannian manifold $(M,g)$ (with analytic Riemannian metric), is the exponential map also analytic everywhere? and Why?

Mohammadreza Bidar
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    The exponential map arises from the solution of different equations, and analytic ODEs have analytic solutions. – Mariano Suárez-Álvarez Jan 28 '18 at 01:59
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    The exponential map is analytic wherever it is defined (since you do not assume completeness of the metric). https://en.wikipedia.org/wiki/Cauchy%E2%80%93Kowalevski_theorem – Moishe Kohan Jan 28 '18 at 11:53

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