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arXiv · 2306.16113

Gromov-Hausdorff limits and Holomorphic isometries

Claudio Arezzo·Chao Li·Andrea Loi
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Abstract

The aim of this paper is to study pointed Gromov-Hausdorff Convergence of sequences of K\"ahler submanifolds of a fixed K\"ahler ambient space. Our result shows that lower bounds on the scalar curvature imply convergence to a smooth K\"ahler manifold satisfying the same curvature bounds, and admitting a holomorphic isometry in the same ambient space. We then apply this convergence result to prove that there are no holomorphic isometries of a non-compact complete K\"ahler manifold with asymptotically non-negative ones into a finite dimensional complex projective space endowed with the Fubini-Study metric.

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Claudio Arezzo, Chao Li, Andrea Loi. 2023-06-28. Gromov-Hausdorff limits and Holomorphic isometries. https://arxiv.org/abs/2306.16113

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