Conformal submanifold geometry I-III

Details Conformal submanifold geometry I-III Conformal submanifold geometry I-III

2010-06-29

arxiv.org/abs/1006.5700v1

Mathematics

Differential Geometry

74 pages

Scientific paper

In Part I, we develop the notions of a Moebius structure and a conformal Cartan geometry, establish an equivalence between them; we use them in Part II to study submanifolds of conformal manifolds in arbitrary dimension and codimension. We obtain Gauss-Codazzi-Ricci equations and a conformal Bonnet theorem characterizing immersed submanifolds of the conformal n-sphere. These methods are applied in Part III to study constrained Willmore surfaces, isothermic surfaces, Guichard surfaces and conformally-flat submanifolds with flat normal bundle, and their spectral deformations, in arbitrary codimension. The high point of these applications is a unified theory of Moebius-flat submanifolds, which include Guichard surfaces and conformally flat hypersurfaces.

Affiliated with

Also associated with

No associations

Rating

Conformal submanifold geometry I-III 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 Conformal submanifold geometry I-III, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conformal submanifold geometry I-III will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-315337