On curve based ruled affine submanifolds

Abstract

In this paper we consider affine ruled submanifolds of arbitrary dimension and codimension in the classical sense, i.e. curve based ones. For such a submanifold we define the natural parameterization and the natural transversal distribution. We calculate all the affine characteristics for such an affine immersion. We find conditions on the base curve and the directions of the rectilinear generators such that the induced connection is flat and the natural transversal distribution is equiaffine.

Keywords

• affine immersion
• equiaffine structure
• ruled submanifild
• flat connection