https://neckpinch.com/authors/angel-j-murcia/New arXiv papers by Ángel J. Murcia, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2305.11069/arxiv:2305.11069Thu, 18 May 2023 00:00:00 GMTAndrei Moroianu, Ángel J. Murcia, C. S. Shahbazi — We introduce a novel curvature flow, the Heterotic-Ricci flow, as the two-loop renormalization group flow of the Heterotic string common sector and study its three-dimensional compact solitons. The Heterotic-Ricci flow is a coupled curvature evolution flow, depending on a non-negative real parameter κ, for a complete Riemannian metric and a three-form H on a manifold M. Its most salient feature is that it involves several terms quadratic in the curvature tensor of a metric connection with skew-symmetric torsion H. When κ= 0 the Heterotic-Ricci flow reduces to the generalized Ricci flow and hence it can be understood as a modification of the latter via the second-order correction prescribed by Heterotic string theory, whereas when H=0 and κ>0 the Heterotic-Ricci flow reduces to a constrained version of the RG-2 flow and hence it can be understood as a generalization of the latter via the introduction of the three-form H. Solutions of Heterotic supergravity with trivial gauge bundle, which we call Heterotic solitons, define a particular class of three-dimensional solitons for the Heterotic-Ricci flow and constitute our main object of study. We prove a number of structural results for three-dimensional Heterotic solitons, obtaining the complete classification of compact three-dimensional strong Heterotic solitons as hyperbolic three-manifolds or quotients of the Heisenberg group equipped with a left-invariant metric. Furthermore, we prove that all Einstein three-dimensional Heterotic solitons have constant dilaton. In this direction, we prove that Einstein Heterotic solitons with constant dilaton are rigid and therefore cannot be deformed into a solution with non-constant dilaton. This is, to the best of our knowledge, the first rigidity result for compact supergravity solutions in the literature.Ricci flowGeneralized & G₂ flowsOther curvature flows3-manifoldsStability & uniquenessPhysics https://neckpinch.com/papers/2109.13906/arxiv:2109.13906Tue, 28 Sep 2021 00:00:00 GMTÁngel Murcia, C. S. Shahbazi — The three-dimensional parallel spinor flow is the evolution flow defined by a parallel spinor on a globally hyperbolic Lorentzian four-manifold. We prove that, despite the fact that Lorentzian metrics admitting parallel spinors are not necessarily Ricci flat, the parallel spinor flow preserves the vacuum momentum and Hamiltonian constraints and therefore the Einstein and parallel spinor flows coincide on common initial data. Using this result, we provide an initial data characterization of parallel spinors on Ricci flat Lorentzian four-manifolds, which in turn yields the first initial data characterization of Ricci-flat pp-waves. Furthermore, we explicitly solve the left-invariant parallel spinor flow on simply connected Lie groups, obtaining along the way necessary and sufficient conditions for the flow to be immortal. These are, to the best of our knowledge, the first non-trivial examples of evolution flows of parallel spinors. Finally, we use some of these examples to construct families of η-Einstein cosymplectic structures and to produce solutions to the left-invariant Ricci flow in three dimensions. This suggests the intriguing possibility of using first-order hyperbolic spinorial flows to construct special solutions of curvature flows in Riemannian signature.Ricci flowOther curvature flowsRicci-flat & Calabi–Yau3-manifolds4-manifoldsHomogeneous spacesLong-time existence & convergenceSasakian & contact geometryPhysics