Levi-Civita Ricci-Flat Metrics on Non-Kähler Calabi-Yau Manifolds

Abstract

We construct new examples of t-Gauduchon Ricci-flat metrics, for all t < 1, on compact non-Kähler Calabi-Yau manifolds defined by certain principal torus bundles over rational homogeneous varieties with Picard number ̺(X) > 1. As an application, we provide a detailed description of new examples of Strominger-Bismut Ricci-flat Hermitian metrics, Lichnerowicz Ricci-flat Hermitian metrics, and balanced Hermitian metrics on principal T 2 -bundles over the Fano threefold È(T È 2 ).