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Existence of higher extremal Kähler metrics on a minimal ruled surface

Sompurkar, RS (2023) Existence of higher extremal Kähler metrics on a minimal ruled surface. In: Bulletin des Sciences Mathematiques, 189 .

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Official URL: https://doi.org/10.1016/j.bulsci.2023.103345


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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