Indefinite equi-centroaffinely homogeneous surfaces with vanishing Pick-invariant in \(\mathbb{R}^ 4\)
type: Item
instance of: scholarly article
title: Indefinite equi-centroaffinely homogeneous surfaces with vanishing Pick-invariant in \(\mathbb{R}^ 4\)
zbMATH Open document ID: 0881.53007
published in: Hokkaido Mathematical Journal
publication date: 1997-05-06T00:00:00Z
review text: The author determines all surfaces in \( \mathbb{R}^4 \) which are homogeneous with respect to the special linear group \(\text{SL} (4,\mathbb{R})\) with indefinite equi-centroaffine metric under the additional assumption of vanishing Pick invariant. Without loss of generality, surfaces contained in an affine hyperplane can be excluded because they are affinely homogeneous in \( \mathbb{R}^3 \). There result 15 cases which are described by explicit parametrizations. In previous papers the author has similarly treated homogeneous surfaces under the side conditions \(K=0\) [\textit{H.-L. Liu}, Result. Math. 29, 280-304 (1996; Zbl 0860.53009)]), resp. \(J=0\) for definite metric [Proc. 1-st Non-Orthodox School on Nonlinearity and Geometry, Warszawa 21-28 September 1995 (Banach Center Publ., Warsaw) (to appear)]. See, also for the 3-dimensional situation, the author's thesis [`Zentroaffine homogene Flächen im \(\mathbb{R}^3\) und \(\mathbb{R}^4\)', TU Berlin (1996)].
reviewed by: Rolf Walter
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 992424
zbMATH Keywords: surface in affine 4-space
zbMATH Keywords: indefinite metric
zbMATH Keywords: Pick invariant
author: Huili Liu
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351257816
OpenAlex ID: W1980657298
DOI: 10.14492/HOKMJ/1351257816
description: scientific article; zbMATH DE number 992424