Conformally Einstein Products and Nearly Kähler Manifolds

Andrei Moroianu (1) , Liviu Ornea (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 UNIBUC - Université de Bucarest

In the first part of this note we study compact Riemannian manifolds (M,g) whose Riemannian product with R is conformally Einstein. We then consider compact 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 regularity assumption) they are obtained as mapping tori of isometries of compact Sasaki-Einstein 5-dimensional manifolds. In particular, we obtain examples of inhomogeneous locally (non-globally) conformal nearly Kähler compact manifolds.

Mots clés: conformally Einstein metrics; nearly Kähler structures; Gray-Hervella classification

Domaines: Géométrie différentielle [math.DG]

Andrei Moroianu, Liviu Ornea. Conformally Einstein Products and Nearly Kähler Manifolds. Annals of Global Analysis and Geometry, 2008, 33 (1), pp.11-18. ⟨10.1007/s10455-007-9071-y⟩. ⟨hal-00108146v4⟩