On the problem of isometry of a hypersurface preserving mean curvature

2007/03/20 by Hülya Bağdatli, Hulya Bagdatli, Bagdatli, Hulya +3
Engineering · Mathematics · #42C15 #46H25 #46L99 #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.DG #msc:42C15 #msc:46H25 #msc:46L99

paper · pdf · doi:10.48550/arxiv.math/0703580

11 pages

arxiv created 2007/03/20 · openalex publication_date 2007/03/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The problem of determining the \it Bonnet hypersurfaces in Rⁿ⁺¹, for n>1, is studied here. These hypersurfaces are by definition those that can be isometrically mapped to another hypersurface or to itself (as locus) by at least one nontrivial isometry preserving the mean curvature. The other hypersurface and/or (the locus of) itself is called \it Bonnet associate of the initial hypersurface. The orthogonal net which is called \hbox\it A-net is special and very important for our study and it is described on a hypersurface. It is proved that, non-minimal hypersurface in Rⁿ⁺¹ with no umbilical points is a Bonnet hypersurface if and only if it has an A-net.

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