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Geodesic orbit and naturally reductive nilmanifolds associated with graphs
Author(s) -
Nikolayevsky Y.
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800456
Subject(s) - mathematics , geodesic , orbit (dynamics) , disjoint sets , invariant (physics) , graph , pure mathematics , metric (unit) , combinatorics , mathematical analysis , mathematical physics , operations management , engineering , economics , aerospace engineering
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.