Annals of Global Analysis and Geometry

, Volume 33, Issue 1, pp 11–18

Conformally Einstein products and nearly Kähler manifolds

Original Paper

DOI: 10.1007/s10455-007-9071-y

Cite this article as:
Moroianu, A. & Ornea, L. Ann Glob Anal Geom (2008) 33: 11. doi:10.1007/s10455-007-9071-y

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 

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