An Extrinsic Look at the Riemannian Hessian
نویسندگان
چکیده
Let f be a real-valued function on a Riemannian submanifold of a Euclidean space, and let f̄ be a local extension of f . We show that the Riemannian Hessian of f can be conveniently obtained from the Euclidean gradient and Hessian of f̄ by means of two manifoldspecific objects: the orthogonal projector onto the tangent space and the Weingarten map. Expressions for the Weingarten map are provided on various specific submanifolds.
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