Abstract
Structure functions constitute the complete set of obstructions to integrability of a G-structure on a manifold. For a Riemannian manifold the structure function is the Riemann tensor. In this work, we compute structure functions for the odd analogue of the metric on supermanifolds and for several related structures. Structure functions take values in Spencer cohomology groups, which we describe by means of the representation theory of Lie algebras and Lie superalgebras.
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Poletaeva, E. Analogues of Riemann tensors for the odd metric on supermanifolds. Acta Appl Math 31, 137–169 (1993). https://doi.org/10.1007/BF00990540
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DOI: https://doi.org/10.1007/BF00990540