A study of the relation between Einstein-Weyl structures and almost contact metric structures

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I used an idea of the Weyl submersion for a research of the Einstein-Weyl structure of a Weyl manifold. For a Weyl submersion with Weyl totally geodesic fibers, I obtained a necessary and sufficient condition for a Weyl structure of the total space to admits an Einstein-Weyl structure. By using its result, I investigated the Einstein-Weyl structure of an η-Einstein contact metric manifold. Moreover, I studied Einstein-Weyl structures of a canonical variation of the total space of a Weyl submersion with Weyl totally geodesic fibers.Next, for a Weyl manifold with a torsion-free affine connection, using the pseudo-Schwarzian tensor I investigated some invariants which do not vary under conformal transformations or Mobius transformations.