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A Hadamard-type open map theorem for submersions and applications to completeness results in control theory. (English) Zbl 1367.46003

The authors give a Hadamard-type theorem for \(C^1\) submersions and then use it to generalize Palais’ Completeness theorem to sub-Riemannian manifolds.

MSC:

46A30 Open mapping and closed graph theorems; completeness (including \(B\)-, \(B_r\)-completeness)
17B66 Lie algebras of vector fields and related (super) algebras
34H05 Control problems involving ordinary differential equations
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
58C25 Differentiable maps on manifolds
93B27 Geometric methods
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References:

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