Foliated vector bundles and Riemannian foliations
Copyright policy )Foliated vector bundles and Riemannian foliations
In this Note we prove the equivalence between the Riemannian foliation and each of the following conditions: 1) the lifted foliation Fr on the bundle of r-transverse jets is Riemannian for r⩾1; 2) the foliation F0r on the slashed J0r is Riemannian and vertically exact for r⩾1; 3) there exists a positively admissible transverse Lagrangian on J0rE, the r-transverse slashed jet bundle of a foliated bundle E→M, for r⩾1.
- University of Craiova Romania
Mathematics - Differential Geometry, FOS: Physical sciences, 53C12, 57R10, 55R10, 55R15, 58A20, Classification of fiber spaces or bundles in algebraic topology, Fiber bundles in algebraic topology, Mathematical Physics (math-ph), fiber bundle, Differential Geometry (math.DG), Riemannian metric, Foliations (differential geometric aspects), FOS: Mathematics, Jets in global analysis, Riemannian foliation, Smoothing in differential topology, bundle of \(r\)-jets, Lagrangian, Mathematical Physics
Mathematics - Differential Geometry, FOS: Physical sciences, 53C12, 57R10, 55R10, 55R15, 58A20, Classification of fiber spaces or bundles in algebraic topology, Fiber bundles in algebraic topology, Mathematical Physics (math-ph), fiber bundle, Differential Geometry (math.DG), Riemannian metric, Foliations (differential geometric aspects), FOS: Mathematics, Jets in global analysis, Riemannian foliation, Smoothing in differential topology, bundle of \(r\)-jets, Lagrangian, Mathematical Physics
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