Calabi-Yau manifolds with $B$-fields

Abstract

In recent work N. Hitchin introduced the concept of "generalised geometry". The key feature of generalised structures is that that they can be acted on by both diffeomorphisms and 2-forms, the so-called $B$-fields. In this lecture, we give a basic introduction and explain some of the fundamental ideas. Further, we discuss some examples of generalised geometries starting from the usual notion of a Calabi-Yau manifold, as well as applications to string theory.

19 pages

References in corpus (2)

• Calibrated cycles and T-duality
• Calibrations on spaces with GxG-structure

Cited by in corpus (2)

• Leibniz algebroids, twistings and exceptional generalized geometry
• Infinitesimal moduli for the Strominger system and Killing spinors in generalized geometry