BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dennis Wulle DTSTART:20240410T160000Z DTEND:20240410T170000Z DTSTAMP:20260423T021221Z UID:VSGS/90 DESCRIPTION:Title: Co homogeneity one manifolds with quasipositive curvature\nby Dennis Wull e as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nLe t $G$ be a Lie group acting by isometries on a Riemannian manifold $(M\,g) $. The action is of cohomogeneity one\, if the orbit space $M/G$ is one-di mensional. In this sense cohomogeneity one manifolds are the most symmetri c manifolds after homogeneous spaces\, which have a $0$-dimensional orbit space. In this talk we will give a classification of cohomogeneity one man ifolds admitting an invariant metric with quasipositive sectional curvatur e\, except for two infinite families in dimension $7$. A Riemannian manifo ld has quasipositive sectional curvature\, if it has non-negative sectiona l curvature and contains one point\, where all tangent planes have positiv e sectional curvature. A similar classification in positive curvature has already been obtained by Verdiani in even dimensions and Grove\, Wilking a nd Ziller in odd dimensions. Surprisingly\, our result only adds two more examples to their list: an Eschenburg space and a Bazaikin space\, which w ere previously known to admit metrics with quasipositive curvature.\n LOCATION:https://researchseminars.org/talk/VSGS/90/ END:VEVENT END:VCALENDAR