Submersion of quaternion CR-submanifolds of a quaternion Kaehler manifold (Q2758283)

Let \(\widetilde{M}\) a quaternion Kähler manifold and \(M\) a quaternion CR-submanifold of \(\widetilde{M}\). In this paper, the authors study submersions \(\pi: M \rightarrow B\) of \(M\) onto an almost quaternion manifold \(B\) satisfying some suitable conditions [as in \textit{S. Kobayashi}, Tôhoku Math. J. (2) 39, 95-100 (1987; Zbl 0619.58004)] for submersions of CR-submanifolds of a Kähler manifold). They prove that \(B\) is also quaternion Kähler and obtain some results when \(M\) is assumed to be CR-product, mixed-foliated, or totally umbilical. Also, the authors give a relation between the sectional curvature of \(\widetilde{M}\) and of the fibres. Further, they investigate the topology of the total space \(M\) of the submersion and obtain a result on de Rham cohomology.