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Conformally Einstein products and nearly Kähler manifolds

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Abstract

In the first part of this note we study compact Riemannian manifolds (M, g) whose Riemannian product with \({\mathbb{R}}\) is conformally Einstein. We then consider 6-dimensional almost Hermitian manifolds of type W 1 + W 4 in the Gray–Hervella classification admitting a parallel vector field and show that (under some mild assumption) they are obtained as Riemannian cylinders over compact Sasaki–Einstein 5-dimensional manifolds.

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Authors and Affiliations

  1. Centre de Mathémathiques, Ecole Polytechnique, 91128, Palaiseau Cedex, France

    Andrei Moroianu

  2. Faculty of Mathematics, University of Bucharest, 14 Academiei str., Bucharest, Romania

    Liviu Ornea

  3. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, RO-014700, Bucharest, Romania

    Liviu Ornea

Authors
  1. Andrei Moroianu
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  2. Liviu Ornea
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Correspondence to Liviu Ornea.

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Moroianu, A., Ornea, L. Conformally Einstein products and nearly Kähler manifolds. Ann Glob Anal Geom 33, 11–18 (2008). https://doi.org/10.1007/s10455-007-9071-y

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  • DOI: https://doi.org/10.1007/s10455-007-9071-y

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