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Winter 2009 Almost-Einstein hypersurfaces in the Euclidean space
Theodoros Vlachos
Illinois J. Math. 53(4): 1221-1235 (Winter 2009). DOI: 10.1215/ijm/1290435347

Abstract

We show that almost-Einstein hypersurfaces in the Euclidean space are homeomorphic to spheres. The proof relies on universal lower bounds in terms of the Betti numbers for the $L^{n/2}$-norms of the Ricci and traceless Ricci tensor of compact oriented $n$-dimensional hypersurfaces. Certain examples show that the assumption on the codimension is essential.

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Theodoros Vlachos. "Almost-Einstein hypersurfaces in the Euclidean space." Illinois J. Math. 53 (4) 1221 - 1235, Winter 2009. https://doi.org/10.1215/ijm/1290435347

Information

Published: Winter 2009
First available in Project Euclid: 22 November 2010

zbMATH: 1213.53072
MathSciNet: MR2741186
Digital Object Identifier: 10.1215/ijm/1290435347

Subjects:
Primary: 53C20 , 53C40
Secondary: 53C42

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign

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Vol.53 • No. 4 • Winter 2009
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