130906 20240319081030.0 doi 10.4310/CAG.2022.v30.n5.a2 sideral 135851 ART-2022-135851 eng Angella, Daniella On Gauduchon connections with Kahler-like curvature 2022 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-85649-P info:eu-repo/grantAgreement/ES/DGA/E22-17R info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 0.7 2022 MATHEMATICS 203 / 329 = 0.617 2022 Q3 T2 0.618 2022 Analysis 2022 Q2 Statistics, Probability and Uncertainty 2022 Q2 Statistics and Probability 2022 Q2 Geometry and Topology 2022 Q2 1.6 2022 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Otal, Antonio (orcid)0000-0002-1567-7159 Ugarte, Luis Universidad de Zaragoza (orcid)0000-0003-2207-8653 Villacampa, Raquel (orcid)0000-0001-6790-7342 2006 440 Universidad de Zaragoza Dpto. Matemáticas Área Geometría y Topología 30, 5 (2022), 961-1006 Commun. anal. geom. COMMUNICATIONS IN ANALYSIS AND GEOMETRY 1019-8385 447511 http://zaguan.unizar.es/record/130906/files/texto_completo.pdf Postprint 1568085 http://zaguan.unizar.es/record/130906/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:130906 articulos driver 2024-03-18-17:05:45 ARTICLE