Loop space of a K\"ahler manifold

M. Anakkar

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arXiv · 2501.15984

Loop space of a K\"ahler manifold

M. Anakkar

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Abstract

We prove that the loop space of a K\"ahler manifold inherits a K\"ahler structure. Then we prove that equipped with this natural metric the loop space is complete and unbounded. Additionally, we show that a geodesic on the loop space can be constructed by piecing together geodesics from each individual leaf.

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BibTeX RIS

M. Anakkar. 2025-01-27. Loop space of a K\"ahler manifold. https://arxiv.org/abs/2501.15984

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