Two-ended hypersurfaces with zero scalar curvature

Jorge Hounie, Maria Luiza Leite

Type: Article

Publication Date: 1999-01-01

Citations: 41

DOI: https://doi.org/10.1512/iumj.1999.48.1664

Abstract

In many ways hypersurfaces with null r-th curvature function H r behave much like the minimal ones (H 1 = 0).One such manifestation is the following result to be proved in this paper, which extends to scalar-flat hypersurfaces (H 2 = 0) a well-known theorem of R. Schoen.Theorem.The only complete scalar-flat embeddings M n ⊂ R n+1 , free of flat points, which are regular at infinity and have two ends, are the hypersurfaces of revolution.

Locations

Indiana University Mathematics Journal - View - PDF

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