Classificação de superfícies com vetor curvatura média normalizado paralelo

Abstract

It is said that a variety Riemannian M2 is a surface with curvature vector average standard parallel if its mean curvature vector is nonzero and the unit vector given this direction is parallel to the normal fi cry . This dissertation demonstrated that In all analytical surface with high curvature normalized vector parallel to or be em E4 or a hypersphere give as a minimum area . Besides that, proof that if a sphere of Riemann in In Vector has average normalized curvature and parallel , then it is in or E3 or a hypersphere of In as a surface minimum.