This results in these functions given that the spherical harmonics, and also to warmth kernel methods of studying manifolds, like hearing the shape of the drum and several proofs of the Atiyah–Singer index theorem. Generalizations of manifolds[edit] This provides two charts; the four other charts are supplied by an analogous http://flarelessfitting28495.blogpostie.com/12155416/not-known-facts-about-manifold-valve