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2001 Parallel affine immersions with maximal codimension
Luc Vrancken
Tohoku Math. J. (2) 53(4): 511-531 (2001). DOI: 10.2748/tmj/1113247798


We study affine immersions, as introduced by Nomizu and Pinkall, of $M^n$ into $\R^{n+p}$. We call $M^n$ linearly full if the image of $M$ is not contained in a lower dimensional affine space. Typical examples of affine immersions are the Euclidean and semi-Riemannian immersions. A classification, under an additional assumption that the rank of the second fundamental form is at least two, of the hypersurfaces with parallel second fundamental form was obtained by Nomizu and Pinkall. If we assume that the second fundamental form is parallel and $M$ is linearly full, then $p \le n(n+1)/2$. In this paper we completely classify the affine immersions with parallel second fundamental form in $\R^{n+n(n+1)/2}$, obtaining amongst others the generalized Veronese immersions.


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Luc Vrancken. "Parallel affine immersions with maximal codimension." Tohoku Math. J. (2) 53 (4) 511 - 531, 2001.


Published: 2001
First available in Project Euclid: 11 April 2005

zbMATH: 1008.53014
MathSciNet: MR1862216
Digital Object Identifier: 10.2748/tmj/1113247798

Primary: 53C42
Secondary: 53A15

Rights: Copyright © 2001 Tohoku University


Vol.53 • No. 4 • 2001
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