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arXiv · 2501.12225

Quaternionic K\"ahler manifolds fibered by solvsolitons

Vicente Cortés·Alejandro Gil-García·Markus Röser
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Abstract

This paper is concerned with the geometry of principal orbits in quaternionic K\"ahler manifolds $M$ of cohomogeneity one. We focus on the complete cohomogeneity one examples obtained from the non-compact quaternionic K\"ahler symmetric spaces associated with the simple Lie groups of type A by the one-loop deformation. We prove that for zero deformation parameter the principal orbits form a fibration by solvsolitons (nilsolitons if $4n=\dim M=4$). The underlying solvable group is non-unimodular if $n>1$ and is the Heisenberg group if $n=1$. We show that under the deformation, the hypersurfaces remain solvmanifolds but cease to be Ricci solitons.

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Vicente Cortés, Alejandro Gil-García, Markus Röser. 2025-01-21. Quaternionic K\"ahler manifolds fibered by solvsolitons. https://arxiv.org/abs/2501.12225

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