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arXiv · 1908.01319

Construction of projective special K\"ahler manifolds

Mauro Mantegazza
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Abstract

In this paper we present an intrinsic characterisation of projective special K\"ahler manifolds in terms of a symmetric tensor satisfying certain differential and algebraic conditions. We show that this tensor vanishes precisely when the structure is locally isomorphic to a standard projective special K\"ahler structure on $\mathrm{SU}(n,1)/\mathrm{S}(\mathrm{U}(n)\mathrm{U}(1))$. We use this characterisation to classify 4-dimensional projective special K\"ahler Lie groups.

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Mauro Mantegazza. 2019-08-04. Construction of projective special K\"ahler manifolds. https://doi.org/10.1007/s10231-021-01096-4

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