Quaternionic submanifolds in quaternionic symmetric spaces
This paper is motivated by a theorem of the author [Tsukuba J. Math. 9, 117-131 (1985; Zbl 0581.53044)], which asserts that a compact quaternionic submanifold in a quaternionic Kähler manifold is homologically volume minimizing. Let M be a quaternionic symmetric space and \({\mathfrak g}\) the Lie algebra of the group of all isometries on M. The classification of quaternionic submanifolds in M is reduced to that of complex simple subalgebras of index 1 in \({\mathfrak g}^{{\mathbb{C}}}\). In the case that M is of classical type quaternionic submanifolds in M are completely classified by the use of the representation theory of complex simple Lie algebras. This classification enables us to investigate the homology classes represented by quaternionic submanifolds.
homologically value minimizing submanifolds
scientific article; zbMATH DE number 3953745