Classification of totally real and totally geodesic submanifolds of compact 3-symmetric spaces
type: Item
instance of: scholarly article
title: Classification of totally real and totally geodesic submanifolds of compact 3-symmetric spaces
zbMATH Open document ID: 1097.53039
author: Koji Tojo
published in: Journal of the Mathematical Society of Japan
publication date: 2006-03-29T00:00:00Z
review text: A 3-symmetric space is a homogeneous Riemannian manifold, which is not a symmetric space, but which admits a geodesic symmetry of order 3 about each point. These spaces were defined by \textit{A. Gray} [J. Differ. Geom. 7, 343--369 (1972; Zbl 0275.53026)]. Using the classification of such spaces [see \textit{J. A. Wolf} and \textit{A. Gray}, J. Differ. Geom., 2, 77--114 (1968; Zbl 0169.24103) and J. Differ. Geom., 2, 115--159 (1968; Zbl 0182.24702)], the author classifies the half-dimensional, totally real, totally geodesic submanifolds of a compact 3-symmetric space.
reviewed by: James Hebda
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C56
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 5015988
zbMATH Keywords: 3-symmetric space
zbMATH Keywords: graded Lie algebra
zbMATH Keywords: totally geodesic submanifold
zbMATH Keywords: affine Lie algebra
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/1145287092
OpenAlex ID: W2078848414
DOI: 10.2969/JMSJ/1145287092
description: scientific article; zbMATH DE number 5015988