129669 20241125101146.0 doi 10.1016/j.geomphys.2023.105014 sideral 135852 ART-2023-135852 eng Otal, Antonio (orcid)0000-0002-1567-7159 Six dimensional homogeneous spaces with holomorphically trivial canonical bundle 2023 Access copy available to the general public Unrestricted We classify all the 6-dimensional unimodular Lie algebras gadmitting a complex structure with non-zero closed (3, 0)-form. This gives rise to 6-dimensional compact homogeneous spaces M= \G, where is a lattice, admitting an invariant complex structure with holomorphically trivial canonical bundle. As an application, in the balanced Hermitian case, we study the instanton condition for any metric connection ∇ε,ρ in the plane generated by the Levi-Civita connection and the Gauduchon line of Hermitian connections. In the setting of the Hull-Strominger system with connection on the tangent bundle being HermitianYang-Mills, we prove that if a compact non-Kähler homogeneous space M= \Gadmits an invariant solution with respect to some non-flat connection ∇in the family ∇ε,ρ, then Mis a nilmanifold with underlying Lie algebra h3, a solvmanifold with underlying algebra g7, or a quotient of the semisimple group SL(2, C). Since it is known that the system can be solved on these spaces, our result implies that they are the unique compact non-Kähler balanced homogeneous spaces admitting such invariant solutions. As another application, on the compact solvmanifold underlying the Nakamura manifold, we construct solutions, on any given balanced Bott-Chern class, to the heterotic equations of motion taking the Chern connection as (flat) instanton. info:eu-repo/grantAgreement/ES/AEI/PID2020-115652GB-I00 info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 1.6 2023 MATHEMATICS 50 / 490 = 0.102 2023 Q1 T1 PHYSICS, MATHEMATICAL 25 / 60 = 0.417 2023 Q2 T2 0.617 2023 Geometry and Topology 2023 Q2 Physics and Astronomy (miscellaneous) 2023 Q2 Mathematical Physics 2023 Q2 2.9 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Ugarte, Luis Universidad de Zaragoza (orcid)0000-0003-2207-8653 2006 440 Universidad de Zaragoza Dpto. Matemáticas Área Geometría y Topología 194 (2023), 105014 [27 pp.] J. geom. phys. JOURNAL OF GEOMETRY AND PHYSICS 0393-0440 690401 http://zaguan.unizar.es/record/129669/files/texto_completo.pdf Versión publicada 2119340 http://zaguan.unizar.es/record/129669/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:129669 articulos driver 2024-11-22-12:04:39 ARTICLE