On minimal homogeneous submanifolds of the hyperbolic space up to codimension two

TL;DR

This paper proves that minimal homogeneous submanifolds of hyperbolic space with codimension up to two are necessarily totally geodesic, extending understanding of their geometric structure.

Contribution

It establishes a classification result for minimal homogeneous submanifolds in hyperbolic space up to codimension two, showing they must be totally geodesic.

Findings

Minimal homogeneous submanifolds of hyperbolic space up to codimension two are totally geodesic.

The result applies to submanifolds with dimension at least 5.

Provides a classification for these submanifolds.

Abstract

We show that a minimal homogeneous submanifold $M^n$, $n\geq 5$, of a hyperbolic space up to codimension two is totally geodesic.