Annals of Global Analysis and Geometry

, Volume 33, Issue 1, pp 11–18

Conformally Einstein products and nearly Kähler manifolds

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 W1 + W4 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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