Deformation of a submanifold in an Euclidean space with fixed Gauss image

In a previous paper [4] the present author studied a C mapping where M is an m-dimensional C manifold, I is some interval and for each tI the mapping is an immersion satisfying the following conditions, (i) The Gauss map associated with the immersion is regular. (ii) The Gauss image of the immersed submanifold is fixed against t for each point p of M. Such a mapping was called an admissible deformation. The purpose of the present paper is to give results obtained since then.