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A gap theorem for positive Einstein metrics on the four-sphere

Akutagawa, Kazuo and Endo, Hisaaki and Seshadri, Harish (2019) A gap theorem for positive Einstein metrics on the four-sphere. In: MATHEMATISCHE ANNALEN, 373 (3-4). pp. 1329-1339.

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Official URL: https://doi.org/10.1007/s00208-018-1749-x

Abstract

We show that there exists a universal positive constant e0 > 0 with the following property: let g be a positive Einstein metric on the four-sphere S4. If the Yamabe constant of the conformal class g] satisfies Y (S4, g]) > 1 v 3 Y (S4, gS]) - e0, where gS denotes the standard round metric on S4, then, up to rescaling, g is isometric to gS. This is an extension ofGursky's gap theorem for positive Einstein metrics on S-4.

Item Type: Journal Article
Additional Information: copyright for this article belongs to SPRINGER HEIDELBERG
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 08 Aug 2019 09:44
Last Modified: 08 Aug 2019 09:44
URI: http://eprints.iisc.ac.in/id/eprint/62888

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