О грассмановом отображении подмногообразий в группах Ли

Abstract

A criterion for the harmonicity of the Grassmann map of an immersed smooth submanifold in some Lie group with left-invariant metric is given. Using the obtained expression, we obtain criteria for the harmonicity of this map in both cases of totally geodesic submanifolds in Lie groups with biinvariant metric and cylindrical submanifolds in Heisenberg groups.