On the geometry of tensor fields on manifolds with almost quaternion structure (Q1269960)

In the last twenty years, many papers have been devoted to the geometry of manifolds that admit subfiberings of fiber bundles of endomorphisms of tangent bundles whose typical fibers are isomorphic either to the algebra of quaternions, antiquaternions, quasiquaternions, or semiquaternions. Let \(M\) be a \(4n\)-dimensional almost quaternionic manifold with a structure \(E\) consisting of tensors of type (1,1) over \(M\) such that in any coordinate neighborhood \(U\) of \(M\) a local basis of almost Hermitian structures \(\theta_1\), \(\theta_2\), \(\theta_3\) satisfies \(\theta_i\circ\theta_j=\theta_k\) with \(\theta_a\circ\theta_b= -\theta_b\circ\theta_a\) for all even permutations \((ijk)\) of \((123)\). In this paper, the author considers the problem of constructing tensor fields and induced structures on submanifolds of manifolds with nonmetric almost quaternion structures. The integrability conditions of these structures are studied.