The classification of projectively homogeneous surfaces. II
type: Item
instance of: scholarly article
title: The classification of projectively homogeneous surfaces. II
zbMATH Open document ID: 0907.53010
author: Takeshi Sasaki
author: Franki Dillen
author: Luc Vrancken
published in: Osaka Journal of Mathematics
publication date: 1999-03-04T00:00:00Z
review text: A submanifold \(M\) in a real projective space is called projectively homogeneous if for any \(p,q\in M\) there exists a projective transformation \(A\) which takes \(p\) to \(q\) and keeps \(M\) invariant. In this paper, the authors give a complete classification of projectively homogeneous surfaces in 3-dimensional real projective space \(P^3\) which are either ruled or degenerate. There are 17 types of such surfaces up to projective transformations in \(P^3\). This work complements the classification of non-ruled and nondegenerate projectively homogeneous surfaces in \(P^3\) given by \textit{K. Nomizu} and \textit{T. Sasaki} [Result. Math. 20, 698-724 (1991; Zbl 0761.53009)] and thus appears as Part II of this paper.
Mathematics Subject Classification ID: 53A20
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 1180580
zbMATH Keywords: real projective 3-space
zbMATH Keywords: classification of projectively homogeneous surfaces
reviewed by: Changping Wang
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1180580