Minimal hyperspheres in two-point homogeneous spaces
type: Item
instance of: scholarly article
title: Minimal hyperspheres in two-point homogeneous spaces
zbMATH Open document ID: 0859.53044
author: Per Tomter
published in: Pacific Journal of Mathematics
publication date: 1996-07-28T00:00:00Z
review text: In this paper existence and uniqueness questions for the case of minimal hyperspheres are studied. The compact two-point homogeneous spaces constitute a natural generalization of classical spherical geometry. These spaces can be characterized as (i) compact two-point homogeneous spaces, (ii) compact rank 1 symmetric spaces, or (iii) irreducible compact positively curved symmetric spaces. The complex projective spaces \(\mathbb{C} P(n)\), the quaternionic projective spaces \(\mathbb{H} P(n)\) and the Cayley projective plane \(\text{Ca}(2)\) are investigated. The following results are obtained: (a) there exist infinitely many congruence classes of imbedded minimal hyperspheres in \(\mathbb{C} P(n)\), \(n\geq 2\), and (b) there exist infinitely many congruence classes of immersed, minimal hyperspheres in \(\mathbb{H} P(n)\), \(n\geq 1\), and in the Cayley projective plane Ca(2).
reviewed by: A. P. Stone
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 910288
zbMATH Keywords: complex projective space
zbMATH Keywords: congruence classes of minimal hyperspheres
zbMATH Keywords: quaternionic projective space
zbMATH Keywords: Cayley projective plane
MaRDI profile type: Publication
full work available at URL: pjm.1996.173.263
OpenAlex ID: W1479873569
DOI: 10.2140/PJM.1996.173.263
description: scientific article; zbMATH DE number 910288