The graded differential geometry of mixed symmetry tensors

Andrew James Bruce and Eduardo Ibarguengoytia

Address: Mathematics Research Unit, University of Luxembourg, Maison du Nombre 6, avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxemburg

E-mail:
andrewjamesbruce@googlemail.com
eduardo.ibarguengoytia@uni.lu

Abstract: We show how the theory of $\mathbb{Z}_2^n$-manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such tensor fields on both flat and curved space-times are discussed.

AMSclassification: primary 53C80; secondary 58A50, 83C65.

Keywords: \mathbb{Z}_2^n-manifolds, mixed symmetry tensors, dual gravitons.

DOI: 10.5817/AM2019-2-123