Double extensions on Riemannian Ricci nilsolitons
type: Item
instance of: scholarly article
title: Double extensions on Riemannian Ricci nilsolitons
zbMATH Open document ID: 1481.53092
author: Zaili Yan
author: Shaoqiang Deng
published in: The Journal of Geometric Analysis
publication date: 2021-09-02T00:00:00Z
review text: Riemannian Ricci solitons are a generalization of Einstein metrics and they were studied by many authors. In pseudo-Riemannian geometry, Einstein metrics are studied in many works. But there are not so many results about pseudo-Riemannian non-Einstein solitons. In the present paper, algebraic Lorentzian Ricci nilsolitons are studied. From a given algebraic Riemannian Ricci nilsoliton, by the process of double extension and using Lorentz data, a Lorentz Ricci nilsoliton in constructed. It is shown that all Lorentz Ricci nilsoliton with degenerate center arise this way. A possibility for classification of these nilsolitons arises. Some particular situations are considered in more detail and examples are given.
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 7389664
zbMATH Keywords: Ricci nilsolitons
zbMATH Keywords: Lorentz metric
zbMATH Keywords: Lorentz datum
zbMATH Keywords: double extension
reviewed by: Zdeněk Dušek
MaRDI profile type: Publication
full work available at URL: s12220-021-00636-x
OpenAlex ID: W3137530017
Wikidata QID: Q115376742
cites work: Structure of homogeneous Riemann spaces with zero Ricci curvature
cites work: Symplectic structures on quadratic Lie algebras
cites work: Free nilpotent Lie algebras admitting ad-invariant metrics
cites work: Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups
cites work: Classification of quadratic Lie algebras of low dimension
cites work: Q4720334
cites work: Q4261815
cites work: On Einstein Lorentzian nilpotent Lie groups
cites work: Four-dimensional pseudo-Riemannian homogeneous Ricci solitons
cites work: Left-Invariant Pseudo-Einstein Metrics on Lie Groups
cites work: Q4830311
cites work: Einstein nilpotent Lie groups
cites work: Ricci-flat and Einstein Pseudoriemannian nilmanifolds
cites work: Indefinite Einstein metrics on simple Lie groups
cites work: A new invariant of quadratic Lie algebras
cites work: Symmetric, invariant, non-degenerate bilinear form on a Lie algebra
cites work: On the structure of symmetric self-dual Lie algebras
cites work: New homogeneous Einstein metrics of negative Ricci curvature
cites work: Noncompact homogeneous Einstein spaces
cites work: Moduli of Einstein and non-Einstein nilradicals
cites work: Q5754632
cites work: Metric Lie algebras with maximal isotropic centre
cites work: Metric Lie algebras and quadratic extensions
cites work: Ricci soliton homogeneous nilmanifolds
cites work: Finding Einstein solvmanifolds by a variational method
cites work: Ricci soliton solvmanifolds
cites work: Einstein solvmanifolds: Existence and non-existence questions
cites work: Groupes de Lie munis de métriques bi-invariantes. (Lie groups admitting bi-invariant metrics)
cites work: Algèbres de Lie et produit scalaire invariant
cites work: Curvatures of left invariant metrics on Lie groups
cites work: Einstein solvmanifolds with a simple Einstein derivation
cites work: Einstein solvmanifolds with free nilradical
cites work: Einstein solvmanifolds and the pre-Einstein derivation
cites work: Einstein solvmanifolds attached to two-step nilradicals
cites work: Left-invariant Lorentz metrics on Lie groups
cites work: Lorentz Ricci solitons on 3-dimensional Lie groups
cites work: Examples of algebraic Ricci solitons in the pseudo-Riemannian case
cites work: Nilsolitons of \(H\)-type in the Lorentzian setting
cites work: Q3312869
cites work: TWO-STEP NILPOTENT LIE ALGEBRAS WITH AD-INVARIANT METRICS AND A SPECIAL KIND OF SKEW-SYMMETRIC MAPS
cites work: The existence of soliton metrics for nilpotent Lie groups
cites work: Lorentz metrics on unimodular Lie groups of dimension three
cites work: Noncompact homogeneous Einstein manifolds attached to graded Lie algebras
cites work: Parabolic subgroups of semisimple Lie groups and Einstein solvmanifolds
cites work: Rank-one Einstein solvmanifolds of dimension 7.
cites work: Einstein metrics on solvable groups
cites work: Pseudo-Riemannian Einstein metrics on noncompact homogeneous spaces
DOI: 10.1007/S12220-021-00636-X
description: scientific article; zbMATH DE number 7389664