Canonical Hermitian Metrics and non-Kähler Calabi–Yau Threefolds

A conifold transition is a process which degenerates 2-cycles and introduces new 3-cycles. We will investigate the web of Calabi–Yau threefolds connected by conifold transitions. Early studies on conifold transitions includes works of Reid and Friedman in the algebraic geometry literature, and Candelas–de la Ossa and Candelas–Green–Hubsch in the physics literature. A conifold transition may connect a Kahler Calabi–Yau to a non-Kahler complex manifold with trivial canonical bundle. There is a also a reverse conifold transition which may produce a non-Kahler symplectic manifold. In this talk, we will discuss the geometrization of these spaces by canonical metrics.