Geodesic orbit and naturally reductive nilmanifolds associated with graphs

Y. Nikolayevsky

Mathematische Nachrichten, 2020, vol. 293, issue 4, 754-760

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.

Date: 2020
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https://doi.org/10.1002/mana.201800456

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