NEW CURVATURE INEQUALITIES FOR HYPERSURFACES IN THE EUCLIDEAN AMBIENT SPACE
| Autor: | Charles T. R. Conley, Rebecca Etnyre, Brady Gardener, Lucy H. Odom, Bogdan D. Suceavă |
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| Rok vydání: | 2013 |
| Předmět: |
surfaces of rotation
Mean curvature flow Mean curvature principal curvatures spread of shape operator General Mathematics 53A30 Mathematical analysis 53B20 extrinsic scalar curvature Center of curvature absolutely umbilical hypersurfaces Curvature 53B25 shape operator Hypersurface Principal curvature Mathematics::Differential Geometry Sectional curvature Scalar curvature Mathematics |
| Zdroj: | Taiwanese J. Math. 17, no. 3 (2013), 885-895 |
| ISSN: | 1027-5487 |
| DOI: | 10.11650/tjm.17.2013.2504 |
| Popis: | The spread of a matrix has been introduced by Mirsky in 1956. The classical theory provides an upper bound for the spread of the shape operator in terms of the second fundamental form of a hypersurface in the Euclidean space. In the present work, we are extending our understanding of the phenomenon by proving a lower bound, inspired from an idea developed recently by X.-Q. Chang. As we are exploring the very concept of curvature on hypersurfaces, we are introducing a new curvature invariant called amalgamatic curvature and we explore its geometric meaning by proving an inequality relating it to the absolute mean curvature of the hypersurface. In our study, a new class of geometric object is obtained: the absolutely umbilical hypersurfaces. |
| Databáze: | OpenAIRE |
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