The Ricci flow approach to homogeneous Einstein metrics on flag manifolds

DOI10.1016/j.geomphys.2011.03.013zbMath1221.53095arXiv1010.3426OpenAlexW2109299899MaRDI QIDQ550305

Ioannis Chrysikos, Stavros Anastassiou

Publication date: 8 July 2011

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.3426

zbMATH Keywords

flag manifoldsnormalized Ricci flowPoincaré compactificationhomogeneous Einstein metrics

Mathematics Subject Classification ID

Related Items (18)

Non-naturally reductive Einstein metrics on exceptional Lie groups ⋮ Ricci flow on certain homogeneous spaces ⋮ Flag manifolds, symmetric \(\mathfrak t\)-triples and Einstein metrics ⋮ The classification of homogeneous Einstein metrics on flag manifolds with \(b_2(M) = 1\) ⋮ Kähler-Ricci flow on rational homogeneous varieties ⋮ Ricci flow on homogeneous spaces with two isotropy summands ⋮ Ricci flow of homogeneous manifolds ⋮ Homogeneous Einstein metrics on non-Kähler C-spaces ⋮ Global behavior of the Ricci flow on generalized flag manifolds with two isotropy summands ⋮ Ricci iteration on homogeneous spaces ⋮ A brief survey on the Ricci flow in homogeneous manifolds ⋮ Maxima of curvature functionals and the prescribed Ricci curvature problem on homogeneous spaces ⋮ The projected homogeneous Ricci flow and its collapses with an application to flag manifolds ⋮ Fractal diffusion from a geometric Ricci flow ⋮ Optimal Curvature Estimates for Homogeneous Ricci Flows ⋮ Ancient solutions of the homogeneous Ricci flow on flag manifolds ⋮ HOMOGENEOUS EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH FIVE ISOTROPY SUMMANDS ⋮ The dynamics of the Ricci flow on generalized Wallach spaces

Cites Work

• Ricci flow on three-dimensional, unimodular metric Lie algebras
• The Ricci flow of left-invariant metrics on full flag manifold \(SU(3)/T\) from a dynamical systems point of view
• Invariant Einstein metrics on flag manifolds with four isotropy summands
• The geometry of compact homogeneous spaces with two isotropy summands
• Motion of charged particles and homogeneous geodesics in Kähler \(C\)-spaces with two isotropy summands
• Existence and non-existence of homogeneous Einstein metrics
• Four-manifolds with positive curvature operator
• Invariant Kähler-Einstein metrics on compact homogeneous spaces
• Invariant Einstein metrics on certain homogeneous spaces
• Three-manifolds with positive Ricci curvature
• Geodesics in reductive homogeneous spaces
• Nonnegatively curved manifolds with finite fundamental groups admit metrics with positive Ricci curvature
• INVARIANT EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH TWO ISOTROPY SUMMANDS
• Characteristic Classes and Homogeneous Spaces, I
• Riemannian flag manifolds with homogeneous geodesics
• Generic Properties of Polynomial Vector Fields at Infinity
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