BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tomoya Tatsuno (University of Oklahoma) DTSTART:20250402T220000Z DTEND:20250402T230000Z DTSTAMP:20260423T021440Z UID:VSGS/108 DESCRIPTION:Title: S ectional Curvature Pinching of Two-Step Nilmanifolds\nby Tomoya Tatsun o (University of Oklahoma) as part of Virtual seminar on geometry with sym metries\n\n\nAbstract\nNilmanifolds are homogeneous Riemannian manifolds a dmitting a transitive nilpotent Lie group of isometries. By classical resu lts (Wolf\, Milnor)\, nilmanifolds are always of mixed curvature. Two-step nilmanifolds are particularly important\, as they play a crucial role in the classification of quarter-pinched homogeneous manifolds of negative cu rvature by Eberlein and Heber. Given a two-step nilmanifold\, we study its pinching constant\, which is the ratio of the minimum and maximum of sect ional curvature.\n\nA prototype of a two-step nilmanifold is the 3-dimensi onal Heisenberg group (so-called Nil). In this case\, it is well known tha t the pinching constant is -3. In this talk\, we show that for any two-ste p nilmanifold\, the pinching constant lies in the compact interval [-3\, - 3/2]. We give examples of two-step nilmanifolds that achieve the bounds -3 and -3/2\, respectively. Moreover\, we discuss why the bounds -3 and -3/2 are special in terms of rigidity.\n LOCATION:https://researchseminars.org/talk/VSGS/108/ END:VEVENT END:VCALENDAR