Geodesic
New properties of prolongations of Linear connections on Weil bundles
Basile Guy Richard Bossoto1 ; Basile Guy Richard Bossoto
1Marien Ngouabi University BP:69 Brazzaville
Acta mathematica Universitatis Comenianae, Tome 85 (2016) no. 1, pp. 69-80 
Basile Guy Richard Bossoto; Basile Guy Richard Bossoto. New properties of prolongations of Linear connections on Weil bundles. Acta mathematica Universitatis Comenianae, Tome 85 (2016) no. 1, pp. 69-80. http://geodesic.mathdoc.fr/item/AMUC_2016_85_1_a5/
@article{AMUC_2016_85_1_a5,
     author = {Basile Guy Richard Bossoto and Basile Guy Richard Bossoto},
     title = { New properties of prolongations of {Linear} connections on {Weil} bundles},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {69--80},
     year = {2016},
     volume = {85},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2016_85_1_a5/}
}
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Voir la notice de l'article provenant de la source Comenius University

Let M be a paracompact smooth manifold, A a Weil algebra and MA the associated Weil bundle. If \nabla is a linear connection on M, we give equivalent denition and the properties of the prolongation \nabla^A to M^A equivalent to the prolongationdened by Morimoto. When (M; g) is a pseudo-riemannian manifold, we show that the symmetric tensor g^A of type (0; 2) dened by Okassa is nondegenerated. At the end, we show that , if \nabla is a Levi-Civita connection on (M; g), then \nabla^A istorsion-free and g^A is parallel with respect to \nabla^A.