Hermitian, pluriclosed metrics with vanishing Bismut-Ricci form give a natural extension of
Calabi-Yau metrics to the setting of complex, non-Kähler manifolds, and arise independently …

We introduce a moment map picture for holomorphic string algebroids where the
Hamiltonian gauge action is described by means of inner automorphisms of Courant …

This book gives an introduction to fundamental aspects of generalized Riemannian,
complex, and K\" ahler geometry. This leads to an extension of the classical Einstein-Hilbert …

In this paper we propose a noncommutative generalization of the relationship between
compact Kähler manifolds and complex projective algebraic varieties. Beginning with a …

We define (p, q) Hermitian geometry as the target space geometry of the two dimensional (p,
q) supersymmetric sigma model. This includes generalised Kähler geometry for (2, 2) …

We formulate an extension of the Calabi conjecture to the setting of generalized K\" ahler
geometry. We show a transgression formula for the Bismut Ricci curvature in this setting …

Under broad hypotheses we derive a scalar reduction of the generalized Kähler–Ricci
soliton system. We realize solutions as critical points of a functional, analogous to the …

On a compact complex manifold $(M, J) $ endowed with a holomorphic Poisson tensor
$\pi_J $ and a deRham class $\alpha\in H^ 2 (M,\mathbb R) $, we study the space of …

Building on works of Boulanger and Goto, we show that Goto's scalar curvature is the
moment map for an action of generalized Hamiltonian automorphisms of the associated …

Generalized Kähler (GK) geometry was discovered in the study of N=(2, 2) supersymmetric σ-
models. In this thesis we develop a new approach to GK geometry by addressing the …