The Totally Umbilical Submanifolds In Spheres And There Applications

Totally umbilical submanifold, nature and features of its predecessors have done a lot in some aspects, the results are fruitful. Many researchers achievements made by our country in this aspect that obtained their own characteristics, there have some influences in our country and all around the world.Effect of the study content theoretical physics, Riemann geometry, complex geometry and other closely related, it has considerable practical significance.In this paper, I mainly defines two Schrodinger operators L1, L2, the first I detailed study the Minimal Submanifolds in sphere and totally umbilical submanifold, and then by the first two characters of the value of operator Estimation of a class of applications of totally umbilical submanifold in ambient space.