Differential Geometry, Lie Theory and Low-Dimensional Topology, Melbourne, Australia, 2016

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Details of talk

TitleThe evolution of positively curved invariant metrics on the Wallach spaces under the Ricci flow
PresenterYurii Nikonorov (Southern Mathematical Institute VSC RAS)
Author(s)Prof Yurii Nikonorov
Sessionn/a
Time
Abstract


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This talk is based on a recent joint paper with N.A.~Abiev ({\it N.A.~Abiev,
Yu.G.~Nikonorov, The evolution of positively curved invariant Riemannian metrics
on the Wallach spaces under the Ricci flow, Annals of Global Analysis and
Geometry, 50:1 (2016), 65--84}).
We studied the evolution of positively curved metrics on the Wallach spaces
$SU(3)/T_{\max}$, $Sp(3)/Sp(1)\times Sp(1)\times Sp(1)$, and $F_4/Spin(8)$.
We proved that for all Wallach spaces, the Ricci flow evolves all generic
invariant Riemannian metrics with positive sectional curvature
into metrics with mixed sectional curvature.
Moreover, we proved that for the spaces $Sp(3)/Sp(1)\times Sp(1)\times Sp(1)$
and $F_4/Spin(8)$, the Ricci flow evolves
all generic invariant Riemannian  metrics with positive Ricci curvature
into metrics with mixed Ricci curvature. We also obtained similar results for
some more general homogeneous spaces.