Six dimensional homogeneous spaces with holomorphically trivial canonical bundle

Otal, Antonio ; Ugarte, Luis (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.geomphys.2023.105014

Año: 2023

Publicado en: JOURNAL OF GEOMETRY AND PHYSICS 194 (2023), 105014 [27 pp.]
ISSN: 0393-0440

Factor impacto JCR: 1.6 (2023)

Categ. JCR: MATHEMATICS rank: 50 / 489 = 0.102 (2023) - Q1 - T1
Categ. JCR: PHYSICS, MATHEMATICAL rank: 25 / 60 = 0.417 (2023) - Q2 - T2

Factor impacto SCIMAGO: 0.617 - Geometry and Topology (Q2) - Physics and Astronomy (miscellaneous) (Q2) - Mathematical Physics (Q2)

Financiación: info:eu-repo/grantAgreement/ES/AEI/PID2020-115652GB-I00

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Geometría y Topología (Dpto. Matemáticas)