On differential-geometric structures on submanifolds of a manifold with an almost quaternionic structure
A manifold \({\mathcal M}_n\) with a pair \((\varphi, \psi)\) of endomorphisms of the tangent bundle \(T {\mathcal M}_n\) for which there hold relations \(\varphi^2 = \psi^2 = -\text{id}\), \(\varphi \circ \psi + \psi \circ \varphi = 0\) is called a manifold with an almost quaternionic structure \({\mathcal M}_n(\varphi, \psi)\). The derivation equations of a normal rigging submanifold \({\mathfrak M}_m \subset {\mathcal M}_n (\varphi, \psi)\) are given. The intersections \({\bigwedge_x}_\varphi = T_x ({\mathcal M}_m) \cap \varphi T_x ({\mathfrak M}_m)\), \({\bigwedge_x}_\psi = T_x ({\mathfrak M}_m) \cap \psi T_x ({\mathfrak M}_m)\), \(x \in {\mathfrak M}_m\) are constructed. If these intersections are not empty, then the submanifold \({\mathfrak M}_m\) is said to be generic. The special classes of generic submanifolds are indicated.
scientific article; zbMATH DE number 795250