Polinomios armónicos y autovalores del Laplaciano sobre la esfera

Abstract

The Laplaciano operator that we know in calculus, has great applications in complex analysis and differential geometry, and from here, the curiosity is born to see how this acts on Riemannian manifold and specifically in the sphere. For which the Hodge * operator is used to give way to the definition of the Laplacian Operator on Riemannian manifold, or the Laplace-Beltrami operator, and with this definition, we proceed to work under local coordinates, so apply it on the sphere and see the behavior of the functions and their eigenvalues on the sphere.