A rigidity theorem of \(\alpha \)-relative parabolic hyperspheres
type: Item
instance of: scholarly article
title: A rigidity theorem of \(\alpha \)-relative parabolic hyperspheres
zbMATH Open document ID: 1380.53016
author: Ruiwei Xu
author: Ling-yun Zhu
published in: Manuscripta Mathematica
publication date: 2017-11-08T00:00:00Z
review text: The authors prove that the only smooth, strictly convex, entire solutions of the equation \[ \text{det} \left( \frac{\partial^2 f}{\partial x_i\partial x_j}\right) = \left(a_{n+1}-\sum a_i\frac{\partial f}{\partial x_i}\right)^\frac{n+2}{\alpha} \;\;\text{ in } \;\;\mathbb{R}^n, \] with \((a_1, a_2, \dots, a_{n+1})\) a constant vector and \(\alpha \notin \left[ \frac{n+2}{n+1}, n+2\right]\), are quadratic polynomials.
reviewed by: Florin Catrina
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 35J60
zbMATH DE Number: 6804017
zbMATH Keywords: \(\alpha\)-relative parabolic affine hypersphere
zbMATH Keywords: Li-geometry
zbMATH Keywords: Blaschke geometry
MaRDI profile type: Publication
full work available at URL: s00229-017-0918-7
OpenAlex ID: W2588413910
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DOI: 10.1007/S00229-017-0918-7
description: scientific article; zbMATH DE number 6804017