doi:10.1515/forum-2012-0072engUgarte, L.Villacampa, R.Balanced hermitian geometry on 6-dimensional nilmanifoldsART-2015-89839The invariant balanced Hermitian geometry of nilmanifolds of dimension 6 is described. We prove that the (restricted) holonomy group of the associated Bismut connection reduces to a proper subgroup of SU(3) if and only if the complex structure is abelian. As an application we show that if J is abelian, then any invariant balanced J-Hermitian structure provides solutions of the Strominger system.2015http://zaguan.unizar.es/record/13106510.1515/forum-2012-0072http://zaguan.unizar.es/record/131065oai:zaguan.unizar.es:131065info:eu-repo/grantAgreement/ES/MICINN/MTM2008-06540-C02-02info:eu-repo/grantAgreement/ES/MICINN/MTM2011-28326-C02-01FORUM MATHEMATICUM 27, 2 (2015), 1025-1070All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess