# Manifolds admitting a metric with co-index of symmetry 4

## TL;DR

This paper classifies compact homogeneous spaces with co-index of symmetry 4 that admit specific metrics, providing explicit examples and a complete characterization of such spaces.

## Contribution

It precisely identifies which compact homogeneous spaces of dimension up to 10 admit metrics with co-index of symmetry 4 and constructs explicit examples.

## Key findings

- Classification of admissible spaces
- Explicit metric examples provided
- Complete characterization of spaces with co-index 4

## Abstract

By a recent result, it is known that compact homogeneous spaces with co-index of symmetry 4 are quotients of a semisimple Lie group of dimension at most 10. In this paper we determine exactly which ones of these spaces actually admit such a metric. For all the admissible spaces we construct explicit examples of these metrics.