Sompurkar, RS (2023) Existence of higher extremal Kähler metrics on a minimal ruled surface. In: Bulletin des Sciences Mathematiques, 189 .
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Abstract
In this paper we prove that on a special type of minimal ruled surface, which is an example of a ‘pseudo-Hirzebruch surface’, every Kähler class admits a certain kind of ‘higher extremal Kähler metric’, which is a Kähler metric whose corresponding top Chern form and volume form satisfy a nice equation motivated by analogy with the equation characterizing an extremal Kähler metric. From an already proven result, it will follow that this specific higher extremal Kähler metric cannot be a ‘higher constant scalar curvature Kähler (hcscK) metric’, which is defined, again by analogy with the definition of a constant scalar curvature Kähler (cscK) metric, to be a Kähler metric whose top Chern form is harmonic. By doing a certain set of computations involving the top Bando-Futaki invariant we will conclude that hcscK metrics do not exist in any Kähler class on this surface. © 2023 Elsevier Masson SAS
| Item Type: | Journal Article |
|---|---|
| Publication: | Bulletin des Sciences Mathematiques |
| Publisher: | Elsevier Masson s.r.l. |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 01 Dec 2023 09:40 |
| Last Modified: | 01 Dec 2023 09:40 |
| URI: | https://eprints.iisc.ac.in/id/eprint/83345 |
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