Rotational Hypersurfaces with Constant Gauss-Kronecker Curvature |
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Authors: | Liu Yuhang Dai Yunchu |
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Institution: | Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China.; Department of Mathematics, Building 380, Stanford University, California 94305, USA. |
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Abstract: | The authors study rotational hypersurfaces with constant Gauss-Kronecker curvature in Rn. They solve the ODE associated with the generating curve of such hypersurface using integral expressions and obtain several geometric properties of such hypersurfaces. In particular, they discover a class of non-compact rotational hypersurfaces with constant and negative Gauss-Kronecker curvature and finite volume, which can be seen as the higher-dimensional generalization of the pseudo-sphere. |
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Keywords: | Differential geometry Gauss-Kronecker curvature Ordinary differential equation |
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