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Study of compact contact manifolds which admit a foliated action. (Spanish) Zbl 1049.53024

A classical question in differential geometry is to study orbits of Lie group actions on differentiable manifolds with some restrictions on the differentiable structure, say, actions which respect some tensor: preserve symplectic forms, contact forms, the volume, etc. In the present work, the author studies structures of contact manifolds \(M^{2m+1}\) on which an action of a Lie group of \({\mathbb R}^{n}\) of foliated structure acts preserving the contact structure. Under this condition, the author proves some estimates on the orbit dimensions.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
58E40 Variational aspects of group actions in infinite-dimensional spaces
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