Stability of minimal submanifolds in symmetric spaces
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.
scientific article; zbMATH DE number 828337