Abstract
The supergravity torsion and curvature constraints are shown to be a particular case of constraints arising in a general geometrical situation. For this purpose, a theorem is proved which describes the necessary and sufficient conditions that the given geometry can be realized on a surface as one induced by the geometry of the ambient space. The proof uses the theory of nonlinear partial differential equations in superspace, Spencer cohomologies, etc. This theorem generalizes various theorems, well known in mathematics (e.g., the Gauss—Codazzi theorem), and may be of its own interest.
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Communicated by Ya. G. Sinai
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Rosly, A.A., Schwarz, A.S. Geometry ofN=1 supergravity (II). Commun.Math. Phys. 96, 285–309 (1984). https://doi.org/10.1007/BF01214576
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DOI: https://doi.org/10.1007/BF01214576