ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 53 Leichtweiß Kurt, Universität Stuttgart, Germany: On the inifinitesimal affine rigidity of ellipsoids in the n-space Due to R. Schneider 1967 an ellipsoid E in the affine space 𝔸^{n} is affinely rigid, i. e. every other ovaloid F in 𝔸^{n} with the same affine Blaschke metric as for E equals E up to an equiaffine motion of E. Due to M. Koszlowski 1985 resp. W. Blaschke 1923 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 up to now for n > 3). – It will be proved that ellipsoids in 𝔸^{n} are also infinitesimally S-rigid for any n. Reference: W. Blaschke, Vorlesungen über Differentialgeometrie II, Springer Verlag Berlin 1923, 90.