Almost quaternionic integral submanifolds and totally umbilic integral submanifolds

摘要

In this work, we consider a Riemannian manifold which admits an integrable distributionwith an almost quaternionic structureV. We show that the torsion tensor of an almost quaternionic structureis independent of the choice of bases. We prove that the integral submanifolds are totally umbilic under the condition of the conjugate shape operatoris skew-adjoint. We give another condition for the shape operatorofto be quaternionic linear.