Riemannian Submersions and Riemannian Manifolds with Einstein--Weyl Structures |
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Authors: | Fumio Narita |
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Institution: | (1) Department of Mathematics, Akita National College of Technology, Akita, 011, Japan |
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Abstract: | The main results of this paper are as follows. (a) Let : 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
be a Riemannian submersion with totally geodesic fibers and N an Einstein manifold of positive scalar curvature
. If M admits a standard Sasakian structure, then M admits an Einstein--Weyl structure with constant Einstein--Weyl function. |
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Keywords: | Riemannian submersion Einstein-Weyl structure Kä hler manifold Sasakian manifold |
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