Harmonic mappings, minimal and totally geodesic immersions of compact Riemannian homogeneous spaces into Grassmann manifolds
Let \(M\) and \(N\) be two compact connected Riemannian manifolds. A smooth mapping \(F : M \to N\) is called harmonic if it is an extremal of the energy. Moreover, if the harmonic mapping \(F : M \to N\) is an isometric immersion, then \(F\) is a minimal immersion. An isometric immersion \(F : M \to N\) is called totally geodesic if \(F\) carries every geodesic of \(M\) to a geodesic of \(N\). A totally geodesic immersion is especially minimal. The existence and construction of minimal immersions and harmonic mappings are interesting and important problems in various situations. In the previous paper [Tsukuba J. Math. 17, No. 1, 169-188 (1993)], we constructed harmonic mappings and minimal immersions from compact Riemannian homogeneous spaces into Grassmann manifolds. In this paper, we study a different construction of harmonic mappings, minimal and totally geodesic immersions of compact Riemannian homogeneous spaces into Grassmann manifolds.
scientific article; zbMATH DE number 515599