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.


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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