Certain Characteristics of the Curvature Tensor of an Affinely Connected Manifold
Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 355-357
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We show how flatness and symmetry of an affinely connected manifold relate themselves to the symmetry of the curvature tensor and its covariant derivative in certain slots. Then we reduce Bianchi first identity to the same form as when the connexion is symmetric; even when the connexion is non-symmetric by considering other conditions.
Sharma, Ramesh. Certain Characteristics of the Curvature Tensor of an Affinely Connected Manifold. Canadian mathematical bulletin, Tome 26 (1983) no. 3, pp. 355-357. doi: 10.4153/CMB-1983-060-0
@article{10_4153_CMB_1983_060_0,
author = {Sharma, Ramesh},
title = {Certain {Characteristics} of the {Curvature} {Tensor} of an {Affinely} {Connected} {Manifold}},
journal = {Canadian mathematical bulletin},
pages = {355--357},
year = {1983},
volume = {26},
number = {3},
doi = {10.4153/CMB-1983-060-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1983-060-0/}
}
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