An intrinsic characterization of a class of minimal surfaces in constant curvature manifolds
type: Item
instance of: scholarly article
title: An intrinsic characterization of a class of minimal surfaces in constant curvature manifolds
zbMATH Open document ID: 0729.53053
author: Gene Douglas Johnson
published in: Pacific Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Let M be a minimal surface in an N-dimensional manifold \(X^ N(c)\) of constant sectional curvature c. Its r-th normal plane is said to be exceptional if a certain condition derived from the structure equations is satisfied. M is called an exceptional minimal surface if all of its normal planes are exceptional. The case M lies fully in \(X^ N(c)\) is considered, namely the case such that for some r the r-th osculating space of M coincides with the tangent space of \(X^ N(c)\) at generic points x of M. Then a sequence of functions \(A^ c_ 1\), \(A^ c_ 2,...\), is constructed on M which characterizes the minimal surface M. When N is odd some relation to the Ricci-Lawson theorem is found [\textit{H. B. Lawson jun.}, Ann. Math., II. Ser. 92, 335-374 (1970; Zbl 0205.520)]. When N is even such surfaces are rigid.
reviewed by: Yosio Mutō
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 4205324
zbMATH Keywords: exceptional normal plane
zbMATH Keywords: minimal surface
zbMATH Keywords: structure equations
zbMATH Keywords: osculating space
zbMATH Keywords: Ricci-Lawson theorem
MaRDI profile type: Publication
full work available at URL: pjm.1991.149.113
OpenAlex ID: W2029121844
DOI: 10.2140/PJM.1991.149.113
description: scientific article; zbMATH DE number 4205324