Stark hypersurfaces in complex projective space

TL;DR

This paper classifies stark hypersurfaces in complex projective space, determining their shape operators and constructing examples in ${ m CP}^2$ using differential systems, advancing understanding of their geometric structure.

Contribution

It completely determines the shape operators for stark hypersurfaces and constructs explicit examples in ${ m CP}^2$ using Frobenius systems.

Findings

Complete classification of shape operators for stark hypersurfaces.

Explicit construction of stark hypersurfaces in ${ m CP}^2$.

Connection between stark hypersurfaces and Frobenius exterior differential systems.

Abstract

Stark hypersurfaces are a special class of austere hypersurface in ${\mathbb C}P^n$ where the shape operator is compatible with the $CR$-structure. In this paper, the possible shape operators for stark hypersurfaces are completely determined, and stark hypersurfaces in ${\mathbb C}P^2$ are constructed as integrals of a Frobenius exterior differential system.