Orbits of s-representations with degenerate Gauss mappings

TL;DR

This paper characterizes tangentially degenerate orbits of s-representations in spheres, showing they occur only through long or short roots of certain root systems, and introduces new examples satisfying the Ferus equality.

Contribution

It provides a complete classification of tangentially degenerate orbits of s-representations and introduces new examples satisfying the Ferus equality.

Findings

Degenerate orbits occur only through specific roots in G_2.

New examples of tangentially degenerate submanifolds are identified.

Characterization of degeneracy conditions for s-representation orbits.

Abstract

In this paper we study tangentially degeneracy of the orbits of s-representations in the sphere. We show that an orbit of an s-representation is tangentially degenerate if and only if it is through a long root, or a short root of restricted root system of type G_2. Moreover these orbits provide many new examples of tangentially degenerate submanifolds which satisfy the Ferus equality.