Conformally invariant bending energy for hypersurfaces

Details Conformally invariant bending energy for hypersurfaces Conformally invariant bending energy for hypersurfaces

2005-07-14

arxiv.org/abs/cond-mat/0507320v1

Physics

Condensed Matter

Soft Condensed Matter

16 pages

Scientific paper

10.1088/0305-4470/38/37/002

The most general conformally invariant bending energy of a closed four-dimensional surface, polynomial in the extrinsic curvature and its derivatives, is constructed. This invariance manifests itself as a set of constraints on the corresponding stress tensor. If the topology is fixed, there are three independent polynomial invariants: two of these are the straighforward quartic analogues of the quadratic Willmore energy for a two-dimensional surface; one is intrinsic (the Weyl invariant), the other extrinsic; the third invariant involves a sum of a quadratic in gradients of the extrinsic curvature -- which is not itself invariant -- and a quartic in the curvature. The four-dimensional energy quadratic in extrinsic curvature plays a central role in this construction.

Affiliated with

Also associated with

No associations

Rating

Conformally invariant bending energy for hypersurfaces 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 Conformally invariant bending energy for hypersurfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conformally invariant bending energy for hypersurfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-574718