Negative Ricci curvature on some non-solvable Lie groups
type: Item
instance of: scholarly article
title: Negative Ricci curvature on some non-solvable Lie groups
zbMATH Open document ID: 1360.53057
author: Cynthia Will
published in: Geometriae Dedicata
publication date: 2017-02-17T00:00:00Z
full work available at URL: http://hdl.handle.net/11336/59979
review text: A construction of new invariant Riemannian metrics on Lie groups (solvable and non-solvable), which have negative Ricci curvature, are given. Non-solvable Lie groups here are the semidirect products \(L= \mathrm{U}(2) \times _{\phi} V\), where \(\phi\) are non-trivial representations and the center of \(\mathrm{U}(2)\) acts on \(V\) by scalar multiplication (as it is noted at the end of this paper, some generalization of this action is possible). The main steps of the construction are connected with two kinds of irreducible linear representations of the compact Lie group \(\mathrm{SU}(2)\). The aforementioned metrics on \(L\) are constructed with aid of metrics with negative Ricci curvature on some solvable Lie groups, which are obtained from \(L\) by the construction of a degeneration.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 6686315
zbMATH Keywords: negative Ricci curvature
zbMATH Keywords: Lie group
zbMATH Keywords: invariant Riemannian metric, solvable Lie group
reviewed by: V. V. Gorbatsevich
MaRDI profile type: Publication
OpenAlex ID: W2510261551
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DOI: 10.1007/S10711-016-0185-X
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description: scientific article; zbMATH DE number 6686315