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.
Citation
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
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