Abstract

This paper  talks about Riemannian Lie subalgebroid. We investigate the induced Levi-civita connection on  Riemannian Lie subalgebroid, and give a construction of the second fondamental form like in case of Riemannian submanifold. We also give the Gauss formula in the case of Riemannian Lie subalgebroid. In the case of the Lie subalgebroid induced by a Leaf of a characteristic foliation, we obtain that the leaf carries more curvature than the manifold as shown by  Boucetta (2011).

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