On Gauduchon connections with Kahler-like curvature

Angella, Daniella ; Otal, Antonio ; Ugarte, Luis (Universidad de Zaragoza) ; Villacampa, Raquel

Resumen: We study Hermitian metrics with a Gauduchon connection being “Kähler-like”, namely, satisfying the same symmetries for curvature as the Levi–Civita and Chern connections. In particular, we investigate dimensional solvmanifolds with invariant complex structures with trivial canonical bundle and with invariant Hermitian metrics. The results for this case give evidence for two conjectures that are expected to hold in more generality: first, if the Strominger–Bismut connection is Kähler-like, then the metric is pluriclosed; second, if another Gauduchon connection, different from Chern or Strominger–Bismut, is Kähler-like, then the metric is Kähler. As a further motivation, we show that the Kähler-like condition for the Levi–Civita connection assures that the Ricci flow preserves the Hermitian condition along analytic solutions.

Idioma: Inglés

DOI: 10.4310/CAG.2022.v30.n5.a2

Año: 2022

Publicado en: COMMUNICATIONS IN ANALYSIS AND GEOMETRY 30, 5 (2022), 961-1006
ISSN: 1019-8385

Factor impacto JCR: 0.7 (2022)

Categ. JCR: MATHEMATICS rank: 203 / 329 = 0.617 (2022) - Q3 - T2

Factor impacto CITESCORE: 1.6 - Mathematics (Q3) - Decision Sciences (Q3)

Factor impacto SCIMAGO: 0.618 - Analysis (Q2) - Statistics, Probability and Uncertainty (Q2) - Statistics and Probability (Q2) - Geometry and Topology (Q2)

Financiación: info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-85649-P
Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-17R

Tipo y forma: Article (PostPrint)

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