A brief survey on the Ricci flow in homogeneous manifolds

Grama, Lino; Martins, Ricardo Miranda

doi:10.1007/s40863-015-0002-8

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“…As mentioned above, to show existence of Einstein metrics is a not an easy task. The use of the normalized Ricci flow on homogeneous spaces towards a qualitative study of homogeneous invariant Einstein metrics, has been used by various authors ( [BW], [GlPa], [AnCh], [GrMa1], [GrMa2], [Bu]) and combined works of N.A. Abiev, A. Arvanitoyeorgos, Yu Nikonorov, and P. Siasos [Ab], [AANS], [AbNi].…”

Section: Introductionmentioning

confidence: 99%

Ricci flow on certain homogeneous spaces

Statha¹

2020

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We study the behavior of the normalized Ricci flow of invariant Riemannian homogeneous metrics at infinity for generalized Wallach spaces, generalized flag manifolds with four isotropy summands and second Betti number equal to one, and the Stiefel manifolds V 2 R n and V 1+k 2 R n , with n = 1 + k 2 + k 3 . We use techniques from the theory of differential equations, in particular the Poincaré compactification. This method allows us to study global phase portraits for polynomial differential systems.

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Section: Introductionmentioning

confidence: 99%