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Hi all, I was wondering what the relationship between the Riemannian Geometry exponential map and the regular manifold exponential map and for the reason behind the name.
What do you mean by "regular manifold exponential map"?Hi all, I was wondering what the relationship between the Riemannian Geometry exponential map and the regular manifold exponential map and for the reason behind the name.
Can you explain the exponential map for a connection on the tangent bundle that is not Levi-Civita?In a manifold with a connection, the exponential map is defined by using the geodesics of that connection (geodesic defined here as a curve for which the derivative of its tangent vector field in the direction of the curve is zero). In a Riemannian manifold, you use a particular connection for this construction, the Levi-Civita connection