$3$-$(\alpha,\delta)$-Sasaki manifolds and strongly positive curvature

Seminar series

Geometry and Analysis Seminar

Date

Mon, 09 Jun 2025
12:15

Location

Speaker

Ilka Agricola

Organisation

Philipps-Universität Marburg

$3$-$(\alpha,\delta)$-Sasaki manifolds are a natural generalisation of $3$-Sasaki manifolds, which in dimension $7$ are intricately related to $G_2$ geometry. We show how these are closely related to various types of quaternionic Kähler orbifolds via connections with skew-torsion and an interesting canonical submersion. Making use of this relation we discuss curvature operators and show that in dimension 7 many such manifolds have strongly positive curvature, a notion originally introduced by Thorpe.