Quelques remarques sur les vari\'et\'es, fonctions de Green et formule de Stokes

TL;DR

This paper discusses various advanced topics in differential geometry, topology, and mathematical physics, including Green functions, Stokes formula, Ricci flow, string theory, and fundamental problems in computational complexity.

Contribution

It provides remarks and insights on multiple complex topics across geometry, physics, and computational theory, connecting them through a unified mathematical perspective.

Findings

Analysis of Green functions and Stokes formula on various manifolds

Discussion of Ricci flow and its applications in geometry

Exploration of fundamental problems in computational complexity

Abstract

We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces of Sobolev spaces, the distance function, the notion of degree and a duality theorem, the variational formulation and conformal map in dimension 2, the metric on the boundary of a Lipschitz domain and polar geodesic coordinates and the Gauss-Bonnet formula and the positive mass theorem in dimension 3 and in the locally conformally flat case. And the Ricci flow. And fields and their relation to the equations.And obstructions in astronomy. And on strings, superstrings and D-branes. And topological solutions in the negative case, critical, supercritical and superstrings and symmetry. And geometrization. And Decision problem, SAT problem and p=np problem.