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math.DG2015
Characterizations of umbilic points of isometric immersions in Riemannian and Lorentzian manifolds
Magdalena Caballero, Rafael M. Rubio
Several characterizations of umbilic points of submanifolds in arbitrary Riemannian and Lorentzian manifolds are given. As a consequence, we obtain new characterizations of spheres…
math.DG2015
A dual rigidity of the sphere and the hyperbolic plane
Magdalena Caballero, Rafael M. Rubio
There are several well-known characterizations of the sphere as a regular surface in the Euclidean space. By means of a purely synthetic technique, we get a rigidity result for the…