Uniqueness theorems in affine differential geometry. I
type: Item
instance of: scholarly article
title: Uniqueness theorems in affine differential geometry. I
zbMATH Open document ID: 0646.53008
DOI: 10.1007/BF03323246
published in: Results in Mathematics
publication date: 1988-01-01T00:00:00Z
review text: [For part II, cf. the review below, Zbl 0646.53009).] This is an interesting paper about equiaffine Weingarten surfaces and hypersurfaces continuing investigations of \textit{A. Švec} [Czech. Math. J. 37, 567-572 (1987)], \textit{R. Schneider} [Math. Z. 101, 375-406 (1967; Zbl 0156.201)] and \textit{A. Schwenk} and the reviewer [Arch. Math. 46, 85-90 (1986; Zbl 0563.53009)]. The author proves a series of uniqueness results about compact locally strongly convex hypersurfaces (with or without boundary). Main tool for the proof are the equiaffine Codazzi equations as partial differential equations (index method, integral formulas). [The reviewer would like to point out that the author meanwhile was able to generalize some of the results of this paper further (to appear).]
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 53C45
zbMATH DE Number: 4054474
zbMATH Keywords: equiaffine Weingarten surfaces
zbMATH Keywords: uniqueness results
zbMATH Keywords: convex hypersurfaces
zbMATH Keywords: equiaffine Codazzi equations
author: An-Min Li
reviewed by: Udo Simon
MaRDI profile type: Publication
Wikidata QID: Q115390773
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full work available at URL: https://doi.org/10.1007/bf03323246
OpenAlex ID: W4205113425
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description: scientific article; zbMATH DE number 4054474