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SUMMARY:Leonardo Cavenaghi (State University of Campinas)
DTSTART:20230726T160000Z
DTEND:20230726T170000Z
DTSTAMP:20260423T021248Z
UID:VSGS/77
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VSGS/77/">Th
 e complete dynamics description of positively curved metrics in the Wallac
 h flag manifold $\\mathrm{SU}(3)/\\mathrm{T}^2$ and other homogeneous spac
 es</a>\nby Leonardo Cavenaghi (State University of Campinas) as part of Vi
 rtual seminar on geometry with symmetries\n\n\nAbstract\nThe family of inv
 ariant Riemannian manifolds in the Wallach flag manifold $\\mathrm{SU}(3)/
 \\mathrm{T}^2$ is described by three parameters $(x\,y\,z)$ of positive re
 al numbers. By restricting such a family of metrics in the tetrahedron $\\
 mathcal{T}:= x+y+z = 1$\, we show how to describe all regions $\\mathcal R
  \\subset \\mathcal T$ admitting metrics with curvature properties varying
  from positive sectional curvature to positive scalar curvature\, includin
 g positive intermediate curvature notion's. We study the dynamics of such 
 regions under the projected Ricci flow in the plane $(x\,y)$\, concluding 
 sign curvature maintenance and escaping. We stress how this approach can b
 e generalized to several other homogeneous spaces and can be helpful to di
 scuss the moduli space of bundles associated with the principal bundle $\\
 mathrm{T}^2\\hookrightarrow \\mathrm{SU}(3) \\rightarrow \\mathrm{SU}(3)/\
 \mathrm{T}^2$.\n\nThis work is done in collaboration with Lino Grama\, Ric
 ardo M. Martins and Douglas D. Novaes\n
LOCATION:https://researchseminars.org/talk/VSGS/77/
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