Hermitian curvature flow on unimodular Lie groups and static invariant metrics

DOI10.1090/tran/8068OpenAlexW3000356678WikidataQ115280241 ScholiaQ115280241MaRDI QIDQ5113207

Ramiro A. Lafuente, Mattia Pujia, Luigi Vezzoni

Publication date: 3 June 2020

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.00059

zbMATH Keywords

homothetiescomplex unimodular Lie groupsleft-invariant soliton solutionstatic Hermitian metrics

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Other connections (53B15) Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows) (53E30)

Related Items (9)

The Search for Solitons on Homogeneous Spaces ⋮ Positive Hermitian curvature flow on special linear groups and perfect solitons ⋮ Hermitian curvature flow on complex locally homogeneous surfaces ⋮ Hermitian curvature flow on compact homogeneous spaces ⋮ Expanding solitons to the Hermitian curvature flow on complex Lie groups ⋮ The anomaly flow on nilmanifolds ⋮ The Hull-Strominger system and the anomaly flow on a class of solvmanifolds ⋮ Positive Hermitian curvature flow on nilpotent and almost-abelian complex Lie groups ⋮ Positive Hermitian curvature flow on complex 2-step nilpotent Lie groups

Cites Work

• Regularity results for pluriclosed flow
• The Ricci flow for simply connected nilmanifolds
• Tamed symplectic forms and strong Kähler with torsion metrics
• Generalized Kähler geometry and the pluriclosed flow
• Einstein solvmanifolds are standard
• Abelian Hermitian geometry
• Special Hermitian metrics and Lie groups
• Hermitian manifolds with zero curvature
• Arithmetic subgroups of algebraic groups
• Cartan decomposition of the moment map
• Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds
• Kähler and symplectic structures on nilmanifolds
• Transitive group actions and Ricci curvature properties
• Curvatures of left invariant metrics on Lie groups
• Lie groups and Lie algebras III. Structure of Lie groups and Lie algebras. Transl. from the Russian by V. Minachin
• On the moment map for the variety of Lie algebras.
• Degenerations of Lie algebras and geometry of Lie groups
• Pluriclosed flow on generalized Kähler manifolds with split tangent bundle
• Immortal homogeneous Ricci flows
• A remark on the Bismut-Ricci form on 2-step nilmanifolds
• Static SKT metrics on Lie groups
• Ricci flow of homogeneous manifolds
• The nondegenerate generalized Kähler Calabi-Yau problem
• Homogeneous Ricci solitons
• Classification of solitons for pluriclosed flow on complex surfaces
• SKT and tamed symplectic structures on solvmanifolds
• Special Hermitian metrics on compact solvmanifolds
• The pluriclosed flow on nilmanifolds and tamed symplectic forms
• Abelian balanced Hermitian structures on unimodular Lie algebras
• Hermitian curvature flow
• Einstein manifolds
• A canonical compatible metric for geometric structures on nilmanifolds
• Structure of homogeneous Ricci solitons and the Alekseevskii conjecture
• Homogeneous solutions of pluriclosed flow on closed complex surfaces
• Vanishing theorems and string backgrounds
• Pluriclosed flow, Born-Infeld geometry, and rigidity results for generalized Kähler manifolds
• Quasi-Kähler Chern-flat manifolds and complex 2-step nilpotent Lie algebras
• ON HOMOGENEOUS RICCI SOLITONS
• Curvature flows for almost-hermitian Lie groups
• Tamed symplectic structures on compact solvmanifolds of completely solvable type
• Convergence of homogeneous manifolds
• On the Chern-Ricci flow and its solitons for Lie groups
• Minimum Vectors for Real Reductive Algebraic Groups
• A note on canonical Ricci forms on $2$-step nilmanifolds
• A Parabolic Flow of Pluriclosed Metrics
• Geometric flows and their solitons on homogeneous spaces
• The Hermitian curvature flow on manifolds with non-negative Griffiths curvature
• The long‐time behavior of the homogeneous pluriclosed flow
• Stratifications with respect to actions of real reductive groups
• Real Geometric Invariant Theory
• Lie groups beyond an introduction
• Complex structures on nilpotent Lie algebras
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Hermitian curvature flow on unimodular Lie groups and static invariant metrics