NEW PROPERTIES OF PROLONGATIONS OF LINEAR CONNECTIONS ON WEIL BUNDLES

Let M be a paracompact smooth manifold, A a Weil algebra and M-A the associated Weil bundle. If del is a linear connection on M, we give equivalent denition and the properties of the prolongation del(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 del is a Levi-Civita connection on (M, g), then del(A) istorsion-free and g(A) is parallel with respect to del(A).