Equigeodesics on full, $G_2$ and a rank-three condition on flag manifolds

TL;DR

This paper characterizes homogeneous geodesics on full G/T and G2 flag manifolds, exploring root systems and providing examples and applications related to sum-zero triples of T-roots.

Contribution

It introduces a new characterization of homogeneous geodesics on specific flag manifolds and examines the property of sum-zero triples of T-roots in generalized root systems.

Findings

Characterization of homogeneous geodesics on full G/T and G2 flag manifolds

Examples illustrating the properties of T-root triples

Applications of sum-zero T-root triples in geometric contexts

Abstract

This paper provides a characterization and examples of homogeneous geodesics on full $G/T$ and $G_{2}$ flag manifolds. We discuss for generalized root systems the property of sum-zero triple of $T$-roots and give several applications of this result.