https://neckpinch.com/authors/vicente-cortes/New arXiv papers by Vicente Cortés, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2611.02062/arxiv:2611.02062Sun, 01 Nov 2026 00:00:00 GMTVicente Cortés, Shubham Dwivedi, Lorenz Jetter — We prove that on a connected, simply-connected nilpotent Lie group, the notions of left-invariant generalized Ricci soliton, semi-algebraic and algebraic generalized Ricci soliton coincide. Moreover, every such soliton has harmonic torsion. We classify all algebraic solitons with positive definite metric on the five-dimensional Heisenberg algebra, the four-dimensional oscillator algebra and the four-dimensional split-oscillator algebra up to automorphisms and rescalings. We find that there is only a finite number of algebraic solitons, all of which have harmonic torsion.Generalized & G₂ flowsRicci solitons4-manifoldsHomogeneous spaces https://neckpinch.com/papers/2501.12225/arxiv:2501.12225Tue, 21 Jan 2025 00:00:00 GMTVicente Cortés, Alejandro Gil-García, Markus Röser — This paper is concerned with the geometry of principal orbits in quaternionic Kähler manifolds M of cohomogeneity one. We focus on the complete cohomogeneity one examples obtained from the non-compact quaternionic Kähler 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.Ricci solitonsKähler geometryHomogeneous spacesBoundaries & non-compact