Šilhan, J., & Gregorovič, J. (2024). The gap phenomenon for conformally related Einstein metrics. Bulletin of the London Mathematical Society, 56(10), 3209–3228. https://doi.org/10.1112/blms.13128
E104-03 - Forschungsbereich Differentialgeometrie und geometrische Strukturen
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Journal:
Bulletin of the London Mathematical Society
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ISSN:
0024-6093
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Date (published):
Oct-2024
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Number of Pages:
20
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Publisher:
WILEY
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Peer reviewed:
Yes
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Keywords:
conformal geometry
en
Abstract:
We determine the submaximal dimensions of the spaces of almost Einstein scales and normal conformal Killing fields for connected conformal manifolds. The results depend on the signature and dimension (Formula presented.) of the conformally nonflat conformal manifold. In definite signature, these two dimensions are at most (Formula presented.) and (Formula presented.), respectively. In Lorentzian signature, these two dimensions are at most (Formula presented.) and (Formula presented.), respectively. In the remaining signatures, these two dimensions are at most (Formula presented.) and (Formula presented.), respectively. This upper bound is sharp and to realize examples of submaximal dimensions, we first provide them directly in dimension 4. In higher dimensions, we construct the submaximal examples as the (warped) product of the (pseudo)-Euclidean base of dimension (Formula presented.) with one of the 4-dimensional submaximal examples.
