The non totally geodesic parallel $2n$-dimensional Kähler submanifolds of the $n$-dimensional quaternionic projective space were classified by K. Tsukada. Here we give the complete classification of non totally geodesic immersions of parallel $2m$-dimensional Kähler submanifolds in a quaternionic Kähler symmetric space of non zero scalar curvature, i.e., in a Wolf space or in its non compact dual. They are exhausted by parallel Kähler submanifolds of a totally geodesic submanifold which is either an Hermitian symmetric space or a quaternionic projective space.
@article{1140727071,
author = {Alekseevsky, Dmitri V. and Di Scala, Antonio J. and Marchiafava, Stefano},
title = {Parallel K\"ahler submanifolds of quaternionic K\"ahler symmetric spaces},
journal = {Tohoku Math. J. (2)},
volume = {57},
number = {1},
year = {2005},
pages = { 521-540},
language = {en},
url = {http://dml.mathdoc.fr/item/1140727071}
}
Alekseevsky, Dmitri V.; Di Scala, Antonio J.; Marchiafava, Stefano. Parallel Kähler submanifolds of quaternionic Kähler symmetric spaces. Tohoku Math. J. (2), Tome 57 (2005) no. 1, pp. 521-540. http://gdmltest.u-ga.fr/item/1140727071/