arXiv subjects
Publications and source records attributed to Thomas Murphy.
We investigate the linear stability of Kähler-Ricci solitons for perturbations induced by varying the complex structure within a fixed Kähler class. We calculate stability for the known examples of Kähler-Ricci solitons.
We introduce curvature-adapted foliations of complex hyperbolic space and study some of their properties. Generalized pseudo-Einstein hypersurfaces of complex hyperbolic space are classified. Analogous results for curvature-adapted hypersurfaces of quaternionic hyperbolic space are also obtained.
We study curvature-adapted submanifolds of general symmetric spaces. We generalize Cartan's theorem for isoparametric hypersurfaces of spheres and Wang's classification of isoparametric Hopf hypersurfaces in complex projective spaces to any compact symmetric space. Our second objective is to investigate such hypersurfaces in some specific symmetric spaces. Various classification results in the Cayley projective and hyperbolic planes and in complex two-plane Grassmannians are obtained under some additional assumptions.
This is a short note proving that Kähler-Ricci solitons with $\dim H^{(1,1)}(M)\ge 2$ are linearly unstable. This extends the results of Cao-Hamilton-Ilmanen in the Kähler-Einstein case.