• SOME PROPERTIES OF SUBMANIFOLDS IN CONFORMAL MANIFOLD

Abstract

In this paper we study the certain properties of submanifold in conformal manifolds. We find some system of quantities which are constitute geometric objects of the submanifold and connected with differential neighborhood of submanifold S^m which is known as fundamental geometric object of submanifold. We prove that the fundamental object of second order of a submanifold S^m allow us to construct the invariant family of central m-spheres and the bundle of tensors. We study the submanifolds carrying a net of curvature lines and also we find the condition that a net of curvature lines on a submanifold S^m is totally holonomic, only m-sphere and hypersurfaces of a conformal manifold can possess an irreducible net of curvature lines.