Relativgeometrische Kennzeichnungen euklidischer Hypersphären. (Characterizations of Euclidean hyperspheres in relative geometry)
The author studies locally strongly convex hypersurfaces of Euclidean n- space. He assumes that a relative normalization is given for them. Extending the geometric calculations initiated by \textit{R. Schneider} [Math. Z. 101, 375-406 (1967; Zbl 0156.201)] he develops integral formulas for the different kinds of curvatures connected with such a normalization and with the second fundamental form. Then, assuming certain inequalities for these curvatures, he uses the integral formulas to derive several interesting local and global geometric characterizations of Euclidean hyperspheres. The results are too complicated to be described here in detail.
characterizations of Euclidean hyperspheres
scientific article; zbMATH DE number 4212912