{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:56:58Z","timestamp":1753883818599,"version":"3.41.2"},"reference-count":42,"publisher":"World Scientific Pub Co Pte Ltd","issue":"14","funder":[{"name":"Portuguese Funds through FCT","award":["UIDB\/MAT\/00013\/2020","UIBP\/MAT\/00013\/2020"],"award-info":[{"award-number":["UIDB\/MAT\/00013\/2020","UIBP\/MAT\/00013\/2020"]}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"crossref","award":["#944448"],"award-info":[{"award-number":["#944448"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Math."],"published-print":{"date-parts":[[2022,12]]},"abstract":"<jats:p> A Hermitian metric on a complex manifold is called SKT (strong K\u00e4hler with torsion) if the Bismut torsion 3-form [Formula: see text] is closed. As the conformal generalization of the SKT condition, we introduce a new type of Hermitian structure, called locally conformal SKT (or shortly LCSKT). More precisely, a Hermitian structure [Formula: see text] is said to be LCSKT if there exists a closed nonzero [Formula: see text]-form [Formula: see text] such that [Formula: see text]. In this paper, we consider nontrivial LCSKT structures, i.e. we assume that [Formula: see text] and we study their existence on Lie groups and their compact quotients by lattices. <\/jats:p><jats:p> In particular, we classify six-dimensional nilpotent Lie algebras admitting a LCSKT structure and we show that, in contrast to the SKT case, there exists a six-dimensional 3-step nilpotent Lie algebra admitting a nontrivial LCSKT structure. Moreover, we show a characterization of even dimensional almost abelian Lie algebras admitting a nontrivial LCSKT structure, which allows us to construct explicit examples of six-dimensional unimodular almost abelian Lie algebras admitting a nontrivial LCSKT structure. The compatibility between the LCSKT and the balanced condition is also discussed, showing that a Hermitian structure on a six-dimensional nilpotent or a [Formula: see text]-dimensional almost abelian Lie algebra cannot be simultaneously LCSKT and balanced, unless it is K\u00e4hler. <\/jats:p>","DOI":"10.1142\/s0129167x22500926","type":"journal-article","created":{"date-parts":[[2022,11,12]],"date-time":"2022-11-12T05:15:09Z","timestamp":1668230109000},"source":"Crossref","is-referenced-by-count":2,"title":["Locally conformal SKT structures"],"prefix":"10.1142","volume":"33","author":[{"given":"Bachir","family":"Djebbar","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed Boudiaf El Mnaouar, Bir El Djir, Oran, 31000 Algeria"}]},{"given":"Ana Cristina","family":"Ferreira","sequence":"additional","affiliation":[{"name":"Centro de Matem\u00e1tica, Universidade do Minho, Campus de Gualtar, 4710-057 Braga, Portugal"}]},{"given":"Anna","family":"Fino","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica \u201cG. Peano\u201d, Universita\u2018 di Torino, Via Carlo Alberto 10, 10123 Torino, Italy"},{"name":"Department of Mathematics and Statistics Florida International University, Miami Florida, 33199, USA"}]},{"given":"Nourhane Zineb Larbi","family":"Youcef","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed Boudiaf El Mnaouar, Bir El Djir, Oran, 31000 Algeria"}]}],"member":"219","published-online":{"date-parts":[[2022,12,9]]},"reference":[{"issue":"3","key":"S0129167X22500926BIB001","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/S0926-2245(01)00044-4","volume":"14","author":"Alexandrov B.","year":"2001","journal-title":"Differ. Geom. 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