On the infinitesimal affine rigidity of ellipsoids in the n-space |
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Authors: | Kurt Leichtweiß |
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Institution: | Memmingerstrasse 14, D-70374 Stuttgart, Germany, DE
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Abstract: | Due to R. Schneider 1967 an ellipsoid E in the affine space
\Bbb An\Bbb A^n is affinely rigid, i.e. every other ovaloid F in
\Bbb An\Bbb A^n with the same affine Blaschke metric as for E equals E up to an equiaffine motion of E. Due to M. Kozlowski 1985 resp. W. Blaschke 1922 for n = 3 ellipsoids are moreover S-rigid resp. infinitesimally S-rigid in the sense of equal resp. infinitesimally equal affine scalar curvature S (unknown until now for n >3). - In this article it is proved that ellipsoids in
\Bbb An\Bbb A^n are also infinitesimally S-rigid for any n. |
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