# On the hypersurfaces contained in their Hessian

## TL;DR

This paper develops a theory of focal loci for hypersurfaces in projective space that are covered by linear spaces with constant tangent spaces, providing new insights into their geometric structure.

## Contribution

It introduces a novel application of focal locus theory to hypersurfaces with special tangent space properties in projective space.

## Key findings

- Characterization of hypersurfaces covered by linear spaces with constant tangent spaces
- Development of a focal locus framework for these hypersurfaces
- New geometric properties derived from the focal locus analysis

## Abstract

This article presents the theory of focal locus applied to the hypersurfaces in the projective space which are (finitely) covered by linear spaces and such that the tangent space is constant along these spaces.