{ "id": "2301.09706", "version": "v1", "published": "2023-01-23T20:24:47.000Z", "updated": "2023-01-23T20:24:47.000Z", "title": "Harmonic complex structures and special Hermitian metrics on products of Sasakian manifolds", "authors": [ "Adrián Andrada", "Alejandro Tolcachier" ], "comment": "Comments are welcome!", "categories": [ "math.DG" ], "abstract": "It is well-known that the product of two Sasakian manifolds carries a 2-parameter family of Hermitian structures $(J_{a,b},g_{a,b})$. We show in this article that the complex structure $J_{a,b}$ is harmonic with respect to $g_{a,b}$, i.e. it is a critical point of the energy functional. Furthermore, we also determine when these Hermitian structures are locally conformally K\\\"ahler, balanced, strong K\\\"ahler with torsion, Gauduchon or $k$-Gauduchon ($k\\geq 2$). Finally, we provide an expression for the Bismut connection associated to $(J_{a,b}, g_{a,b})$ in terms of the characteristic connections on each Sasakian factor.", "revisions": [ { "version": "v1", "updated": "2023-01-23T20:24:47.000Z" } ], "analyses": { "subjects": [ "53C15", "53C25", "53D15" ], "keywords": [ "harmonic complex structures", "special hermitian metrics", "hermitian structures", "sasakian manifolds carries", "sasakian factor" ], "note": { "typesetting": "TeX", "pages": 0, "language": "en", "license": "arXiv", "status": "editable" } } }