Conformally Einstein Products and Nearly Kähler Manifolds

Details Conformally Einstein Products and Nearly Kähler Manifolds Conformally Einstein Products and Nearly Kähler Manifolds

2006-10-19

arxiv.org/abs/math/0610599v4

Annals of Global Analysis and Geometry 33, 1 (2008) 11-18

Mathematics

Differential Geometry

Scientific paper

10.1007/s10455-007-9071-y

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 K\"ahler compact manifolds.

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