Deformation of Kähler Metrics and an Eigenvalue Problem for the Laplacian on a Compact Kähler Manifold
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909404470706176 |
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| author | Narita, Kazumasa |
| author_facet | Narita, Kazumasa |
| contents | We study an eigenvalue problem for the Laplacian on a compact Kähler manifold. Considering the $k$-th eigenvalue $λ_{k}$ as a functional on the space of Kähler metrics with fixed volume on a compact complex manifold, we introduce the notion of $λ_{k}$-extremal Kähler metric. We deduce a condition for a Kähler metric to be $λ_{k}$-extremal. As examples, we consider product Kähler manifolds, compact isotropy irreducible homogeneous Kähler manifolds and flat complex tori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06261 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Deformation of Kähler Metrics and an Eigenvalue Problem for the Laplacian on a Compact Kähler Manifold Narita, Kazumasa Differential Geometry We study an eigenvalue problem for the Laplacian on a compact Kähler manifold. Considering the $k$-th eigenvalue $λ_{k}$ as a functional on the space of Kähler metrics with fixed volume on a compact complex manifold, we introduce the notion of $λ_{k}$-extremal Kähler metric. We deduce a condition for a Kähler metric to be $λ_{k}$-extremal. As examples, we consider product Kähler manifolds, compact isotropy irreducible homogeneous Kähler manifolds and flat complex tori. |
| title | Deformation of Kähler Metrics and an Eigenvalue Problem for the Laplacian on a Compact Kähler Manifold |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2304.06261 |