Affine hypersurfaces admitting a pointwise SO(n-1) symmetry

TL;DR

This paper classifies strictly locally convex affine hypersurfaces in Euclidean space that exhibit pointwise SO(n-1) symmetry, focusing on their geometric structure and invariance properties.

Contribution

It provides a comprehensive classification of affine hypersurfaces with pointwise SO(n-1) symmetry, expanding understanding of their geometric invariants and structure.

Findings

Classification of hypersurfaces with SO(n-1) symmetry

Description of geometric invariants under the symmetry group

Characterization of convexity conditions

Abstract

In this article we obtain a classification of strictly locally convex affine hypersurfaces in A^{n+1} for which the geometrical structure is pointwise invariant under the group SO(n-1) represented by rotations around a fixed axis in the tangent space.