The vectorial Ribaucour transformation for submanifolds and applications

Details The vectorial Ribaucour transformation for submanifolds and applications The vectorial Ribaucour transformation for submanifolds and applications

2005-08-12

arxiv.org/abs/math/0508217v1

Mathematics

Differential Geometry

24 pages

Scientific paper

In this paper we develop the vectorial Ribaucour transformation for Euclidean submanifolds. We prove a general decomposition theorem showing that under {appropriate} conditions the composition of two or more vectorial Ribaucour transformations is again a vectorial Ribaucour transformation. An immediate consequence of this result is the classical permutability of Ribaucour transformations. Our main application is an explicit local construction of all Euclidean submanifolds with flat normal bundle. Actually, this is a particular case of a more general result. Namely, we obtain a local explicit construction of all Euclidean submanifolds carrying a parallel flat normal subbundle, in particular of all those that carry a parallel normal vector field. Finally, we describe all submanifolds carrying a Dupin principal curvature normal vector field with integrable conullity, a concept that has proven to be crucial in the study of reducibility of Dupin submanifolds.

Affiliated with

Also associated with

No associations

Rating

The vectorial Ribaucour transformation for submanifolds and applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The vectorial Ribaucour transformation for submanifolds and applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The vectorial Ribaucour transformation for submanifolds and applications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-38573