Geodesic orbit and naturally reductive nilmanifolds associated with graphs

Abstract

We study Riemannian nilmanifolds associated with graphs. We prove that such a nilmanifold is geodesic orbit if and only if it is naturally reductive if and only if its defining graph is the disjoint union of complete graphs and the left-invariant metric is generated by a certain naturally defined inner product.

9 pages, 1 figure

Cited by in corpus (1)

• Automorphism Groups of nilpotent Lie algebras associated to certain graphs