Einstein nilpotent Lie groups

DOI10.1016/j.jpaa.2018.05.010zbMath1407.53076arXiv1707.04454OpenAlexW2734981088WikidataQ115345383 ScholiaQ115345383MaRDI QIDQ1621581

Diego Conti, Federico Alberto Rossi

Publication date: 9 November 2018

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.04454

zbMATH Keywords

Ricci tensormoment mapnilpotent Lie groupsRicci-flat metricsEinstein pseudo-Riemannian metrics

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Nilpotent and solvable Lie groups (22E25) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Momentum maps; symplectic reduction (53D20)

Related Items (13)

A non Ricci-flat Einstein pseudo-Riemannian metric on a 7-dimensional nilmanifold ⋮ Classification of Einstein Lorentzian 3-nilpotent Lie groups with 1-dimensional nondegenerate center ⋮ New pseudo Einstein metrics on Einstein solvmanifolds ⋮ Left invariant Ricci flat metrics on Lie groups ⋮ Pseudo-Kähler and pseudo-Sasaki structures on Einstein solvmanifolds ⋮ On Einstein Lorentzian nilpotent Lie groups ⋮ Construction of nice nilpotent Lie groups ⋮ Existence of left invariant Ricci flat metrics on nilpotent Lie groups ⋮ Double extensions on Riemannian Ricci nilsolitons ⋮ Pseudo-algebraic Ricci solitons on Einstein nilradicals ⋮ Indefinite Einstein metrics on nice Lie groups ⋮ Ricci-flat and Einstein Pseudoriemannian nilmanifolds ⋮ Indefinite nilsolitons and Einstein solvmanifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Four-dimensional Lorentzian Lie groups
• Einstein solvmanifolds: Existence and non-existence questions
• Nilmanifolds with a calibrated \(G_{2}\)-structure
• Einstein solvmanifolds are standard
• Groupes de Lie munis de métriques bi-invariantes. (Lie groups admitting bi-invariant metrics)
• On the nilpotent Lie algebras of dimension \(\leq 7)\)
• Existence and non-existence of homogeneous Einstein metrics
• Ricci curvature of left invariant metrics on solvable unimodular Lie groups
• On the varieties of nilpotent Lie algebras of dimension 7 and 8
• Curvatures of left invariant metrics on Lie groups
• Noncompact homogeneous Einstein spaces
• The minimum principle from a Hamiltonian point of view
• The Ricci tensor of almost Parahermitian manifolds
• A variational approach for compact homogeneous Einstein manifolds
• Non-existence of homogeneous Einstein metrics
• Indefinite Einstein metrics on nice Lie groups
• Compact pseudo-Riemannian homogeneous Einstein manifolds of low dimension
• Isometric actions on pseudo-Riemannian nilmanifolds
• Einstein manifolds
• A canonical compatible metric for geometric structures on nilmanifolds
• Torsion-free \(G^*_{2(2)}\)-structures with full holonomy on nilmanifolds
• Para-Hermitian and paraquaternionic manifolds
• On the diagonalization of the Ricci flow on Lie groups
• Split Special Lagrangian Geometry
• Homogeneous para-Kähler Einstein manifolds
• Indefinite Einstein metrics on simple Lie groups
• Vector fields and Ricci curvature

This page was built for publication: Einstein nilpotent Lie groups