Abstract
Regarding the theory of foliation, some aspects of the theory of Riemannian foliations have been brought in completion by the Molino theory. Such a structure is defined by some finite dimensional Lie subalgebra of the Lie algebra of transverse vector fields. The problem I am interested in is more modeste. It is to get sufficient conditions for a smooth manifold admitting foliations with transverse (pseudo) Riemannian metrics. The investigation is inspired by both methods of information geometry and the Hessian geometry.
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