Surfaces in 3-space possessing nontrivial deformations which preserve the shape operator

Details Surfaces in 3-space possessing nontrivial deformations which preserve the shape operator Surfaces in 3-space possessing nontrivial deformations which preserve the shape operator

2001-07-17

arxiv.org/abs/math/0107122v1

Mathematics

Differential Geometry

17 pages, to appear in the Proccedings of the conference "Integrable Systems in Differential Geometry", Tokyo, July 2000

Scientific paper

The class of surfaces in 3-space possessing nontrivial deformations which preserve principal directions and principal curvatures (or, equivalently, the shape operator) was investigated by Finikov and Gambier as far back as in 1933. We review some of the known examples and results, demonstrate the integrability of the corresponding Gauss-Codazzi equations and draw parallels between this geometrical problem and the theory of compatible Poisson brackets of hydrodynamic type. It turns out that coordinate hypersurfaces of the n-orthogonal systems arising in the theory of compatible Poisson brackets of hydrodynamic type must necessarily possess deformations preserving the shape operator.

Affiliated with

Also associated with

No associations

Rating

Surfaces in 3-space possessing nontrivial deformations which preserve the shape operator 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 Surfaces in 3-space possessing nontrivial deformations which preserve the shape operator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Surfaces in 3-space possessing nontrivial deformations which preserve the shape operator will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-642826