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Analogues of Riemann tensors for the odd metric on supermanifolds. (English) Zbl 0795.53025

Author’s abstract: “Structure functions constitute the complete set of obstructions to the 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”.
Reviewer: R.Schmid (Atlanta)

MSC:

53C10 \(G\)-structures
53B20 Local Riemannian geometry
58A50 Supermanifolds and graded manifolds
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