Generalized duality for k-forms

Details Generalized duality for k-forms Generalized duality for k-forms

2011-09-05

arxiv.org/abs/1109.0894v1

J. Geom. Phys. 61 (2011) no. 12, 2293-2308

Mathematics

Differential Geometry

Scientific paper

10.1016/j.geomphys.2011.07.007

We give the definition of a duality that is applicable to arbitrary $k$-forms. The operator that defines the duality depends on a fixed form $\Omega$. Our definition extends in a very natural way the Hodge duality of $n$-forms in $2n$ dimensional spaces and the generalized duality of two-forms. We discuss the properties of the duality in the case where $\Omega$ is invariant with respect to a subalgebra of $\mathfrak{so}(V)$. Furthermore, we give examples for the invariant case as well as for the case of discrete symmetry.

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