Totally geodesic submanifolds of Damek–Ricci spaces

Sinhwi Kim; Yuri Nikolayevsky; JeongHyeong Park

doi:10.4171/rmi/1228

JournalsrmiVol. 37, No. 4pp. 1321–1332

Totally geodesic submanifolds of Damek–Ricci spaces

Sinhwi Kim
Sungkyunkwan University, Suwon, Republic of Korea
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- zbMATH Open
Yuri Nikolayevsky
La Trobe University, Melbourne, Australia
- MathSciNet
- zbMATH Open
JeongHyeong Park
Sungkyunkwan University, Suwon, Republic of Korea
- MathSciNet
- zbMATH Open

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Abstract

We classify totally geodesic submanifolds of Damek–Ricci spaces and show that they are either subgroups (“smaller” Damek–Ricci spaces) or isometric to rank-one symmetric spaces of negative curvature.

Cite this article

Sinhwi Kim, Yuri Nikolayevsky, JeongHyeong Park, Totally geodesic submanifolds of Damek–Ricci spaces. Rev. Mat. Iberoam. 37 (2021), no. 4, pp. 1321–1332

DOI 10.4171/RMI/1228