Stability of minimal submanifolds in symmetric spaces
type: Item
instance of: scholarly article
title: Stability of minimal submanifolds in symmetric spaces
zbMATH Open document ID: 0837.53045
author: Makiko S. Tanaka
published in: Tsukuba Journal of Mathematics
publication date: 1996-05-13T00:00:00Z
review text: Given a compact Riemannian symmetric space \(M\), there associate basic totally geodesic submanifolds of \(M\), called the polars and the meridians (equivalently, the \(M_+\)'s and the \(M_-\)'s) of \(M\). The polars and the meridian of a compact Riemannian symmetric space were introduced and studied in [\textit{B. Y. Chen} and \textit{T. Nagano}, Duke Math. J. 45, 405- 425 (1978; Zbl 0384.53024)]. The stability of the polars and the meridian of some compact symmetric spaces were first investigated by the reviewer, P. F. Leung and T. Nagano in 1980 [cf. the reviewer, Geometry of slant submanifolds, Leuven: Kath. Univ. Leuven, Dept. of Mathematics, 123 p. (1990; Zbl 0716.53006)]. The method of Chen-Leung-Nagano was improved and reformulated by \textit{Y. Ohnita} in [Compos. Math. 64, 157-189 (1987; Zbl 0634.53041)]. In this paper, the author investigates the basic properties of polars and meridians of compact symmetric spaces further. In particular, she determines the stability of polars and meridians of most compact symmetric spaces. Moreover, she obtains many interesting new properties of polars and meridians of compact Riemannian symmetric spaces.
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C42
zbMATH DE Number: 828337
zbMATH Keywords: \((M^ +, M^ -)\)-method
zbMATH Keywords: \((M^ +, M^ -)\)-theory
zbMATH Keywords: polar
zbMATH Keywords: meridian
zbMATH Keywords: compact symmetric spaces
zbMATH Keywords: stability
reviewed by: Bang-Yen Chen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.21099/tkbjm/1496162798
OpenAlex ID: W2289259987
DOI: 10.21099/TKBJM/1496162798
description: scientific article; zbMATH DE number 828337