# Geodesic orbit Riemannian spaces with two isotropy summands. I

## TL;DR

This paper classifies compact simply connected geodesic orbit Riemannian spaces with two isotropy summands, advancing understanding of their geometric structure and symmetry properties.

## Contribution

It provides a complete classification of such spaces with two irreducible isotropy submodules, a significant step in the study of geodesic orbit spaces.

## Key findings

- Classification of compact simply connected geodesic orbit spaces with two isotropy summands.
- Identification of the structure of these spaces based on isotropy representation.
- Enhanced understanding of the symmetry properties of geodesic orbit Riemannian spaces.

## Abstract

The paper is devoted to the study of geodesic orbit Riemannian spaces that could be characterize by the property that any geodesic is an orbit of a 1-parameter group of isometries. The main result is the classification of compact simply connected geodesic orbit Riemannian spaces $G/H$ with two irreducible submodules in the isotropy representation.