Abstract
The main results of this paper are as follows. (a) Let π : M → N be a non-trivial Riemannian submersion with totally geodesic fibers of dimension 1 over an Einstein manifold N. If M is compact and admits a standard Einstein--Weyl structure with constant Einstein--Weyl function, then N admits a Kähler structure andM a Sasakian structure. (b) Let \( \pi:{M^{2n + 1} \to N^{2n}} \) be a Riemannian submersion with totally geodesic fibers and N an Einstein manifold of positive scalar curvature \( \geqslant 4n(n + 1)\). If M admits a standard Sasakian structure, then M admits an Einstein--Weyl structure with constant Einstein--Weyl function.
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Narita, F. Riemannian Submersions and Riemannian Manifolds with Einstein--Weyl Structures. Geometriae Dedicata 65, 103–116 (1997). https://doi.org/10.1023/A:1004988728034
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DOI: https://doi.org/10.1023/A:1004988728034