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Differential Geometry Seminar
The Hitchin and Einstein indices of cohomogeneity one nearly Kähler manifolds
The Hitchin and Einstein indices of cohomogeneity one nearly Kähler manifolds
Organizers
Speaker
Time
Tuesday, October 28, 2025 3:00 PM - 4:00 PM
Venue
A7-201
Online
Zoom 388 528 9728
(BIMSA)
Abstract
Nearly Kähler manifolds are Riemannian 6-manifolds admitting real Killing spinors. They are the cross-sections of Riemannian cones with holonomy G2. Like the Einstein equation, the nearly Kähler condition has a variational interpretation in terms of volume functionals, first introduced by Hitchin in 2001.
The existence problem for nearly Kähler manifolds is poorly understood, and the only currently known inhomogeneous examples were found in 2017 by Foscolo and Haskins using cohomogeneity one methods. For one of their examples, we establish non-trivial bounds on the coindex of the Hitchin-type and Einstein functionals. We do this by analysing the eigenvalue problem for the Laplacian on coclosed primitive (1,1)-forms under a cohomogeneity-one symmetry assumption.
The existence problem for nearly Kähler manifolds is poorly understood, and the only currently known inhomogeneous examples were found in 2017 by Foscolo and Haskins using cohomogeneity one methods. For one of their examples, we establish non-trivial bounds on the coindex of the Hitchin-type and Einstein functionals. We do this by analysing the eigenvalue problem for the Laplacian on coclosed primitive (1,1)-forms under a cohomogeneity-one symmetry assumption.