Estimates For Eigenvalues Of A Class Of Schr(?)dinger Operators On Curvature Submanifolds With Constant Mean Curvature

Curvature submanifold is a generalization of curvature line in surface theory.In this paper,we study the first eigenvalues of a class of Schr(?)dinger operators on curva-ture submanifolds,and give their upper bounds.Specifically,let:(?)(?)dimensional compact curvature submanifold in(?)with constant mean curvature,the principal curvature of(?),andis the square of length of the second fundamental form of(?),then we get the following conclusions:(1)IfH=0,M~n is a minimal curvature submanifolds,let(?)be the first eigen-value of Schr(?)dinger operator(?),then(?)is totally geodesic.(2)Letbe an9)-dimensional compact curvature hypersurface with non-zero con-stant curvature H,and P=1.Let(?)be the first eigenvalue of Schr(?)dinger operator(?).Then(?)The results generalize some results of Wu[20]and Chen[12].