Vector fields on n-foliated 2n-dimensional manifolds
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In this paper, we study basic differential invariants of the pair (vector field, foliation). As a result, we establish a dynamic interpretation and a generalization of the Levi-Civita connection and Riemannian curvature treated as invariants of the geodesic flow on the tangent bundle.
KeywordsManifold Vector Field Tangent Bundle Riemannian Curvature Geodesic Flow
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