Rosly, A. A.; Schwarz, A. S. Geometry of \(N=1\) supergravity. (English) Zbl 0644.53077 Commun. Math. Phys. 95, 161-184 (1984). [For part II, see the review below.] \(N=1\) supergravity can be formulated in superspace in a number of different ways. There is a whole family of supergravity theories parametrized by \(\xi\). Meanwhile, various geometric approaches to superspace are also being pursued. In this paper, the authors use the induced G-structure [the second author, ibid. 87, 37–63 (1982; Zbl 0503.53048)] to continue the study of the geometry of \(N=1\) supergravities. A new geometrical formalism is suggested for the nonminimal and minimal supergravities and this formalism interconnects the constrained with the unconstrained superspace formulations and is based on the notion of induced geometry. A clear geometrical content of torsion and curvature constraints is exhibited. Reviewer: K. K. Lee (M.R. 86a:83086) Cited in 1 ReviewCited in 4 Documents MSC: 53C80 Applications of global differential geometry to the sciences 83E50 Supergravity Keywords:supergravity; G-structure; superspace formulations; torsion; curvature Citations:Zbl 0644.53078; Zbl 0503.53048 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Wess, J., Zumino, B.: Superspace formulation of supergravity. Phys. Lett.66B, 361-364 (1977); Superfield Lagrangian for supergravity. Phys. Lett.74B, 51-53 (1978) [2] Siegel, W., Gates, S.J.: Superfield supergravity. Nucl. Phys. B147, 77-104 (1979) · doi:10.1016/0550-3213(79)90416-4 [3] Gates, S.J., Siegel, W.: Understanding constraints in superspace formulations of supergravity. Nucl. Phys. B163, 519-545 (1980) · doi:10.1016/0550-3213(80)90414-9 [4] Stelle, K.S., West, P.C.: Minimal auxiliary fields for supergravity. Phys. Lett.74B, 330-332 (1978) [5] Ferrara, S., van Nieuwenhuizen, P.: The auxiliary fields of supergravity. Phys. 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