Invariant Calabi-Yau structures on punctured complexified symmetric spaces

Naoyuki Koike

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arXiv · 2003.04118

Invariant Calabi-Yau structures on punctured complexified symmetric spaces

Naoyuki Koike

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Abstract

In this paper, we show that $G$-invariant Calabi-Yau structures on the complexification $G^{\mathbb C}/K^{\mathbb C}$ of a symmetric space $G/K$ of compact type are constructed from solutions of a Monge-Amp$\grave{\rm e}$re type equation. Also, we give an explicit descriptions of the Monge-Amp$\grave{\rm e}$re type equation in the case where the rank of $G/K$ is equal to one or two. Furthermore, we prove the existence of solutions of the Monge-Amp$\grave{\rm e}$re type equation.

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Naoyuki Koike. 2020-03-09. Invariant Calabi-Yau structures on punctured complexified symmetric spaces. https://arxiv.org/abs/2003.04118

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