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2015 Totally geodesic subalgebras in 2-step nilpotent Lie algebras
Rachelle C. Decoste, Lisa Demeyer
Rocky Mountain J. Math. 45(5): 1425-1444 (2015). DOI: 10.1216/RMJ-2015-45-5-1425


We describe totally geodesic subalgebras of a metric 2-step nilpotent Lie algebra $\n$. We prove that a totally geodesic subalgebra of $\n$ is either abelian and flat or can be decomposed as a direct sum determined by the curvature transformation. In addition, we give conditions under which a totally geodesic submanifold of a simply connected 2-step nilpotent Lie group is a totally geodesic subgroup. We follow Eberlein's 1994 paper in which he imposes the condition of nonsingularity on $\n$. We remove this restriction and illustrate the distinction between the nonsingular case and the unrestricted case.


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Rachelle C. Decoste. Lisa Demeyer. "Totally geodesic subalgebras in 2-step nilpotent Lie algebras." Rocky Mountain J. Math. 45 (5) 1425 - 1444, 2015.


Published: 2015
First available in Project Euclid: 26 January 2016

zbMATH: 1334.53041
MathSciNet: MR3452221
Digital Object Identifier: 10.1216/RMJ-2015-45-5-1425

Primary: 22E25 , 53C30

Keywords: Two-step nilpotent Lie algebra and totally geodesic subalgebra

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium


Vol.45 • No. 5 • 2015
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