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Annals of Global Analysis and Geometry

, Volume 33, Issue 1, pp 11–18 | Cite as

Conformally Einstein products and nearly Kähler manifolds

  • Andrei Moroianu
  • Liviu Ornea
Original Paper

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.

Keywords

Conformally Einstein metrics Nearly Kähler structures Gray–Hervella classification 

Mathematics Subject Classification (2000)

Primary 53C15 53C25 53A30 

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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Centre de MathémathiquesEcole PolytechniquePalaiseau CedexFrance
  2. 2.Faculty of MathematicsUniversity of BucharestBucharestRomania
  3. 3.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania

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