000130906 001__ 130906 000130906 005__ 20240319081030.0 000130906 0247_ $$2doi$$a10.4310/CAG.2022.v30.n5.a2 000130906 0248_ $$2sideral$$a135851 000130906 037__ $$aART-2022-135851 000130906 041__ $$aeng 000130906 100__ $$aAngella, Daniella 000130906 245__ $$aOn Gauduchon connections with Kahler-like curvature 000130906 260__ $$c2022 000130906 5060_ $$aAccess copy available to the general public$$fUnrestricted 000130906 5203_ $$aWe 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. 000130906 536__ $$9info:eu-repo/grantAgreement/ES/AEI-FEDER/MTM2017-85649-P$$9info:eu-repo/grantAgreement/ES/DGA/E22-17R 000130906 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000130906 590__ $$a0.7$$b2022 000130906 591__ $$aMATHEMATICS$$b203 / 329 = 0.617$$c2022$$dQ3$$eT2 000130906 592__ $$a0.618$$b2022 000130906 593__ $$aAnalysis$$c2022$$dQ2 000130906 593__ $$aStatistics, Probability and Uncertainty$$c2022$$dQ2 000130906 593__ $$aStatistics and Probability$$c2022$$dQ2 000130906 593__ $$aGeometry and Topology$$c2022$$dQ2 000130906 594__ $$a1.6$$b2022 000130906 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000130906 700__ $$0(orcid)0000-0002-1567-7159$$aOtal, Antonio 000130906 700__ $$0(orcid)0000-0003-2207-8653$$aUgarte, Luis$$uUniversidad de Zaragoza 000130906 700__ $$0(orcid)0000-0001-6790-7342$$aVillacampa, Raquel 000130906 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000130906 773__ $$g30, 5 (2022), 961-1006$$pCommun. anal. geom.$$tCOMMUNICATIONS IN ANALYSIS AND GEOMETRY$$x1019-8385 000130906 8564_ $$s447511$$uhttps://zaguan.unizar.es/record/130906/files/texto_completo.pdf$$yPostprint 000130906 8564_ $$s1568085$$uhttps://zaguan.unizar.es/record/130906/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000130906 909CO $$ooai:zaguan.unizar.es:130906$$particulos$$pdriver 000130906 951__ $$a2024-03-18-17:05:45 000130906 980__ $$aARTICLE