Double extensions on Riemannian Ricci nilsolitons

DOI10.1007/s12220-021-00636-xzbMath1481.53092OpenAlexW3137530017WikidataQ115376742 ScholiaQ115376742MaRDI QIDQ1979225

Shaoqiang Deng, Zaili Yan

Publication date: 2 September 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-021-00636-x

zbMATH Keywords

Lorentz metricdouble extensionLorentz datumRicci nilsolitons

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50)

Related Items (5)

Ricci solitons on four-dimensional Lorentzian Lie groups ⋮ The structure of geodesic orbit Lorentz nilmanifolds ⋮ Left invariant Ricci flat metrics on Lie groups ⋮ Existence of left invariant Ricci flat metrics on nilpotent Lie groups ⋮ Indefinite nilsolitons and Einstein solvmanifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Einstein solvmanifolds attached to two-step nilradicals
• Examples of algebraic Ricci solitons in the pseudo-Riemannian case
• Algebraic Ricci solitons of three-dimensional Lorentzian Lie groups
• Einstein solvmanifolds: Existence and non-existence questions
• Moduli of Einstein and non-Einstein nilradicals
• Parabolic subgroups of semisimple Lie groups and Einstein solvmanifolds
• A new invariant of quadratic Lie algebras
• Metric Lie algebras and quadratic extensions
• Einstein solvmanifolds with a simple Einstein derivation
• The existence of soliton metrics for nilpotent Lie groups
• Groupes de Lie munis de métriques bi-invariantes. (Lie groups admitting bi-invariant metrics)
• Symmetric, invariant, non-degenerate bilinear form on a Lie algebra
• Lorentz metrics on unimodular Lie groups of dimension three
• Structure of homogeneous Riemann spaces with zero Ricci curvature
• Curvatures of left invariant metrics on Lie groups
• Left-invariant Lorentz metrics on Lie groups
• Noncompact homogeneous Einstein spaces
• Rank-one Einstein solvmanifolds of dimension 7.
• Metric Lie algebras with maximal isotropic centre
• Einstein nilpotent Lie groups
• Einstein metrics on solvable groups
• Finding Einstein solvmanifolds by a variational method
• Free nilpotent Lie algebras admitting ad-invariant metrics
• Ricci-flat and Einstein Pseudoriemannian nilmanifolds
• On Einstein Lorentzian nilpotent Lie groups
• Pseudo-Riemannian Einstein metrics on noncompact homogeneous spaces
• Symplectic structures on quadratic Lie algebras
• Einstein solvmanifolds with free nilradical
• Noncompact homogeneous Einstein manifolds attached to graded Lie algebras
• Nilsolitons of H-type in the Lorentzian setting
• Left-Invariant Pseudo-Einstein Metrics on Lie Groups
• Einstein solvmanifolds and the pre-Einstein derivation
• Ricci soliton solvmanifolds
• Classification of quadratic Lie algebras of low dimension
• Algèbres de Lie et produit scalaire invariant
• Indefinite Einstein metrics on simple Lie groups
• Four-dimensional pseudo-Riemannian homogeneous Ricci solitons
• On the structure of symmetric self-dual Lie algebras
• TWO-STEP NILPOTENT LIE ALGEBRAS WITH AD-INVARIANT METRICS AND A SPECIAL KIND OF SKEW-SYMMETRIC MAPS
• New homogeneous Einstein metrics of negative Ricci curvature
• Ricci soliton homogeneous nilmanifolds
• Lorentz Ricci solitons on 3-dimensional Lie groups

This page was built for publication: Double extensions on Riemannian Ricci nilsolitons