Deformation of K\"{a}hler Metrics and an Eigenvalue Problem for the Laplacian on a Compact K\"{a}hler Manifold
We study an eigenvalue problem for the Laplacian on a compact K\"{a}hler manifold. Considering the $k$-th eigenvalue $\lambda_{k}$ as a functional on the space of K\"{a}hler metrics with fixed volume on a compact complex manifold, we introduce the notion of $\lambda_{k}$-extremal K\"{...
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Main Author | |
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Format | Journal Article |
Language | English |
Published |
13.04.2023
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Subjects | |
Online Access | Get full text |
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Summary: | We study an eigenvalue problem for the Laplacian on a compact K\"{a}hler
manifold. Considering the $k$-th eigenvalue $\lambda_{k}$ as a functional on
the space of K\"{a}hler metrics with fixed volume on a compact complex
manifold, we introduce the notion of $\lambda_{k}$-extremal K\"{a}hler metric.
We deduce a condition for a K\"{a}hler metric to be $\lambda_{k}$-extremal. As
examples, we consider product K\"{a}hler manifolds, compact isotropy
irreducible homogeneous K\"{a}hler manifolds and flat complex tori. |
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DOI: | 10.48550/arxiv.2304.06261 |