The Discriminant of the Second Fundamental Forms Under Connection Preserving Map

Abstract

Let : f : E-n -> E-n be an isometric immersion provided f(M) = (M) over bar where M and (M) over bar are (n -1)-dimensional Riemannian manifolds. We study the discriminant of the second fundamental forms and also being lambda - isotropic of the Riemannian manifolds if f is a connection preserving map.