5 citations · 9 across the 15 of their papers we have counts for
16 papers
PhySGA: A Physics-Space Grounded Agentic Framework for Generalizable and Interactive 3D Composition
Weichen Lyu, Chong Xia, Mingyu Dong +3
3D object composition is pivotal to digital content creation and robot simulation, while also serving as a critical testbed for physical intelligence in foundation models. Previous…
Kenmotsu manifolds and spin-c Killing spinors
José Luis Carmona Jiménez, Alejandro Gil-García, C. S. Shahbazi
Using the theory of complex spinorial forms, we prove that an odd-dimensional Riemannian manifold admits a pure spin-c Killing spinor with an imaginary Killing function if and…
Torsion parallel pure spinors on neutral manifolds
Alejandro Gil-García
We study irreducible real pure spinors on pseudo-Riemannian manifolds of neutral signature using the theory of real spinorial forms. We prove that the square of such a spinor is a…
Sasakian manifolds and spin-c Killing spinors
Alejandro Gil-García, C. S. Shahbazi
Using the theory of complex spinorial forms, we prove that an odd-dimensional Riemannian manifold admits a pure spin-c Killing spinor with a real Killing constant $α\in\mathbb{R}^{…
Complex spinorial forms, Brinkmann four-manifolds, and self-dual bundle gerbes
Alejandro Gil-García, C. S. Shahbazi
We develop the differential theory of complex spinorial forms associated with irreducible complex spinors across all dimensions and signatures. This framework enables the study of…
Left-invariant harmonic spinors on three-dimensional Lie groups
Alejandro Gil-García, Giovanni Russo
We study the existence of left-invariant harmonic spinors on three-dimensional Lie groups equipped with a left-invariant pseudo-Riemannian metric. An existing formula for the spin…
The algebraic square of an irreducible complex spinor
Alejandro Gil-García, C. S. Shahbazi
We characterize, in every dimension and signature, the algebraic squares of an irreducible complex spinor as a pair of exterior forms satisfying a prescribed system of algebraic re…
Almost abelian pseudo-Kähler Lie algebras
Diego Conti, Alejandro Gil-García
We study invariant pseudo-Kähler structures on a solvmanifold such that the Lie algebra is almost abelian, that is ,…
Quaternionic Kähler manifolds fibered by solvsolitons
Vicente Cortés, Alejandro Gil-García, Markus Röser
This paper is concerned with the geometry of principal orbits in quaternionic Kähler manifolds of cohomogeneity one. We focus on the complete cohomogeneity one examples obtaine…
Born Lie algebras
Alejandro Gil-García, Paula Naomi Pilatus
We show that every Born Lie algebra can be obtained by the bicross product construction starting from two pseudo-Riemannian Lie algebras. We then obtain a classification of all Lie…
Parallel spinors for and isotropic structures
Alejandro Gil-García, C. S. Shahbazi
We obtain a correspondence between irreducible real parallel spinors on pseudo-Riemannian manifolds of signature and solutions of an associated differential system…
Symmetries of one-loop deformed q-map spaces
Vicente Cortés, Alejandro Gil-García, Danu Thung
Q-map spaces form an important class of quaternionic Kähler manifolds of negative scalar curvature. Their one-loop deformations are always inhomogeneous and have been used to const…
Pseudo-Kähler and hypersymplectic structures on semidirect products
Diego Conti, Alejandro Gil-García
We study left-invariant pseudo-Kähler and hypersymplectic structures on semidirect products ; we work at the level of the Lie algebra .…
Moduli spaces of (co)closed -structures on nilmanifolds
Giovanni Bazzoni, Alejandro Gil-García
We compute the dimensions of some moduli spaces of left-invariant closed and coclosed -structures on 7-dimensional nilmanifolds, showing that they are not related to…
A class of locally inhomogeneous complete quaternionic Kähler manifolds
Vicente Cortés, Alejandro Gil-García, Arpan Saha
We prove that the one-loop deformation of any quaternionic Kähler manifold in the class of c-map spaces is locally inhomogeneous. As a corollary, we obtain that the full isometry g…
Symmetric and skew-symmetric complex structures
Giovanni Bazzoni, Alejandro Gil-García, Adela Latorre
On a complex manifold , we interpret complex symplectic and pseudo-Kähler structures as symplectic forms with respect to which is, respectively, symmetric and skew-symme…