• On the Problem of Isometry of a Hypersurface Preserving Mean Curvature-Erratum

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/117/01/0049-0059

• # Keywords

Bonnet hypersurface; Bonnet associate; isometry; mean curvature; preserving; Bonnet curve; 𝐴-net.

• # Abstract

The problem of determining the Bonnet hypersurfaces in $R^{n+1}$, for $n&gt;1$, 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.

• # Author Affiliations

1. Department of Mathematics, Marmara University, Istanbul, Turkey
2. Department of Mathematics, Yıldız Technical University, Istanbul, Turkey

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019