3-dimensional affine hypersurfaces admitting a pointwise SO(2)- or Z_3-symmetry

Details 3-dimensional affine hypersurfaces admitting a pointwise SO(2)- or Z_3-symmetry 3-dimensional affine hypersurfaces admitting a pointwise SO(2)- or Z_3-symmetry

2003-03-07

arxiv.org/abs/math/0303099v1

Mathematics

Differential Geometry

22 pages, preprint from Oct. 7, 2002

Scientific paper

In (equi-)affine differential geometry, the most important algebraic invariants are the affine (Blaschke) metric h, the affine shape operator S and the difference tensor K. A hypersurface is said to admit a pointwise symmetry if at every point there exists a linear transformation preserving the affine metric, the affine shape operator and the difference tensor K. The study of submanifolds which admit pointwise isometries was initiated by Bryant (math.DG/0007128). In this paper, we consider the 3-dimensional positive definite hypersurfaces for which at each point the group of symmetries is isomorphic to either Z_3 or SO(2). We classify such hypersurfaces and show how they can be constructed starting from 2-dimensional positive definite affine spheres.

Affiliated with

Also associated with

No associations

Rating

3-dimensional affine hypersurfaces admitting a pointwise SO(2)- or Z_3-symmetry 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 3-dimensional affine hypersurfaces admitting a pointwise SO(2)- or Z_3-symmetry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and 3-dimensional affine hypersurfaces admitting a pointwise SO(2)- or Z_3-symmetry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-719880