BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Nazia Valiyakath (Syracuse University)
DTSTART:20260225T160000Z
DTEND:20260225T170000Z
DTSTAMP:20260423T040046Z
UID:VSGS/126
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VSGS/126/">O
 n nilpotent and solvable quasi-Einstein manifolds</a>\nby Nazia Valiyakath
  (Syracuse University) as part of Virtual seminar on geometry with symmetr
 ies\n\n\nAbstract\nIn this talk\, I will discuss the classification of qua
 si-Einstein metrics on nilpotent and unimodular solvable Lie groups. Focus
 ing on quasi-Einstein metrics $(M\,g\,X)$ for which the metric $g$ and the
  vector field $X$ are left-invariant—what we call totally left-invariant
  quasi-Einstein metrics—I will first present a complete classification i
 n the nilpotent case. In particular\, I will show that a nilpotent Lie gro
 up admits such a metric if and only if it is Heisenberg.\n\nI will then tu
 rn to unimodular solvable Lie groups and show that the existence of a non-
 flat totally left-invariant quasi-Einstein metric imposes strong structura
 l restrictions\, forcing the center of the group to be one-dimensional. Un
 der the additional assumption that the adjoint action is given by a normal
  derivation\, I will describe a full classification: the Lie group must be
  standard and its nilradical necessarily Heisenberg. As an application\, I
  will explain why the only near-horizon geometries arising on nilmanifolds
  are quotients $\\Gamma \\backslash H_n$ of the Heisenberg group.\n
LOCATION:https://researchseminars.org/talk/VSGS/126/
END:VEVENT
END:VCALENDAR