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We describe the Special Kahler structure on the base of the so-called Hitchin system in terms of the geometry of the space of spectral curves. It yields a simple formula for the Kahler potential. This extends to the case of a singular spectral curve and we show that this defines the Special Kahler structure on certain natural integrable subsystems. Examples include the extreme case where the metric is flat.
A special Kahler-Ricci potential on a Kahler manifold is any nonconstant $C^infty$ function $tau$ such that $J( ablatau)$ is a Killing vector field and, at every point with $dtau e 0$, all nonzero tangent vectors orthogonal to $ ablatau$ and $J( abla
In this paper, we introduce the coupled Ricci iteration, a dynamical system related to the Ricci operator and twisted Kahler-Einstein metrics as an approach to the study of coupled Kahler-Einstein (CKE) metrics. For negative first Chern class, we pro
We study the quantization of coupled Kahler-Einstein (CKE) metrics, namely we approximate CKE metrics by means of the canonical Bergman metrics, so called the ``balanced metrics. We prove the existence and weak convergence of balanced metrics for the
We review results about $G_2$-structures in relation to the existence of special metrics, such as Einstein metrics and Ricci solitons, and the evolution under the Laplacian flow on non-compact homogeneous spaces. We also discuss some examples in detail.
We construct balanced metrics on the family of non-Kahler Calabi-Yau threefolds that are obtained by smoothing after contracting $(-1,-1)$-rational curves on Kahler Calabi-Yau threefold. As an application, we construct balanced metrics on complex man