Identificador persistente para citar o vincular este elemento:
http://hdl.handle.net/10662/12306
Títulos: | Ancient solutions of the homogeneous Ricci ow on ag manifolds |
Autores/as: | Anastassiou, S. Chrysikos, I. |
Palabras clave: | Ricci flow;Homogeneous spaces;Flag manifolds;Ancient solutions;Scalar curvature;Flujo de Ricci;Espacios homogéneos;Colectores de bandera;Soluciones antiguas;Curvatura escalar |
Fecha de publicación: | 2021 |
Editor/a: | Universidad de Extremadura |
Resumen: | For any flag manifold M=G/K of a compact simple Lie group G we describe non-collapsing ancient invariant solutions of the homogeneous unnormalized Ricci flow. Such solutions emerge from an invariant Einstein metric on M, and by [13] they must develop a Type I singularity in their extinction finite time, and also to the past. To illustrate the situation we engage ourselves with the global study of the dynamical system induced by the unnormalized Ricci flow on any flag manifold M=G/K with second Betti number b2(M) = 1, for a generic initial invariant metric. We describe the corresponding dynamical systems and present non-collapsed ancient solutions, whose α-limit set consists of fixed points at infinity of MG. Based on the Poincaré compactification method, we show that these fixed points correspond to invariant Einstein metrics and we study their stability properties, illuminating thus the structure of the system’s phase space. |
Descripción: | - Czech Science Foundation. Project GA_CR no. 19-14466Y |
URI: | http://hdl.handle.net/10662/12306 |
DOI: | 10.17398/2605-5686.36.1.99 |
Colección: | Extracta Mathematicae Vol. 36, nº 1 (2021) |
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