Affine curvature of plane geodesic lines on affine hypersurfaces
We establish a necessary and sufficient condition for a geodesic line on a nondegenerate hypersurface to be a plane curve. We deduce a formula for the affine curvature of a plane geodesic line on the affine hypersurface in terms of the affine fundamental form and the shape operator. We present the d...
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| Date: | 2017 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2017
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1716 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We establish a necessary and sufficient condition for a geodesic line on a nondegenerate hypersurface to be a plane curve.
We deduce a formula for the affine curvature of a plane geodesic line on the affine hypersurface in terms of the affine
fundamental form and the shape operator. We present the definition of transverse curvature and determine some of its
elementary properties. |
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