A lemma of Élie Cartan
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- by Robert Maltz PDF
- Proc. Amer. Math. Soc. 53 (1975), 433-434 Request permission
Abstract:
We provide in this paper an alternative proof of the lemma of E. Cartan which states that parallel translation of curvature and torsion locally determines an affine connection. Our proof uses covariant differentiation of tensor fields over mappings in place of Cartan’s exterior differential calculus.References
- Richard L. Bishop and Samuel I. Goldberg, Tensor analysis on manifolds, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1968. MR 0224010
- D. Gromoll, W. Klingenberg, and W. Meyer, Riemannsche Geometrie im Grossen, Lecture Notes in Mathematics, No. 55, Springer-Verlag, Berlin-New York, 1968 (German). MR 0229177, DOI 10.1007/978-3-540-35901-2
- Robert Maltz, Isometric immersions into spaces of constant curvature, Illinois J. Math. 15 (1971), 490–502. MR 282317
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 433-434
- MSC: Primary 53B05
- DOI: https://doi.org/10.1090/S0002-9939-1975-0410582-7
- MathSciNet review: 0410582