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

dc.creatorScharlach, Christine
dc.creatorVrancken, Luc
dc.date2003-03-07
dc.date.accessioned2026-07-07T04:55:52Z
dc.date.available2026-07-07T04:55:52Z
dc.descriptionIn (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.
dc.description22 pages, preprint from Oct. 7, 2002
dc.identifierhttps://arxiv.org/abs/math/0303099
dc.identifierhttp://arxiv.org/abs/math/0303099
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66732
dc.subjectDifferential Geometry
dc.subject53A15
dc.title3-dimensional affine hypersurfaces admitting a pointwise SO(2)- or Z_3-symmetry
dc.typetext

Files

Collections