On the problem of isometry of a hypersurface preserving mean curvature |
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Authors: | Hülya Bağdatli Ziya Soyuçok |
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Institution: | (1) Department of Mathematics, Marmara University, Istanbul, Turkey;(2) Department of Mathematics, Yıldız Technical University, Istanbul, Turkey |
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Abstract: | The problem of determining the Bonnet hypersurfaces in R
n+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 Bonnet associate of the initial hypersurface.
The orthogonal net which is called 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 R
n+1 with no umbilical points is a Bonnet hypersurface if and only if it has an A-net. |
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Keywords: | Bonnet hypersurface Bonnet associate isometry mean curvature preserving Bonnet curve A-net |
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