Totally geodesic submanifolds of the homogeneous nearly K\"ahler 6-manifolds and their G2-cones

TL;DR

This paper classifies totally geodesic submanifolds within homogeneous nearly Kähler 6-manifolds and their G2-cones, introducing new techniques for analyzing such submanifolds in various Riemannian contexts.

Contribution

It develops novel methods for studying totally geodesic submanifolds in analytic Riemannian manifolds, homogeneous spaces, and Riemannian cones, including an example with self-intersections.

Findings

Classification of totally geodesic submanifolds in nearly Kähler 6-manifolds

Development of new analytical techniques for Riemannian submanifold study

Example of a self-intersecting totally geodesic submanifold

Abstract

In this article we classify totally geodesic submanifolds of homogeneous nearly K\"ahler 6-manifolds, and of the G2-cones over these 6-manifolds. To this end, we develop new techniques for the study of totally geodesic submanifolds of analytic Riemannian manifolds, naturally reductive homogeneous spaces, and Riemannian cones. In particular, we obtain an example of a totally geodesic submanifold with self-intersections in a simply connected homogeneous space.