Almost quaternionic integral submanifolds and totally umbilic integral submanifolds

In literature (Kobayashi and Nomizu, 1963, 1969; Yano and Ako, 1972; Ishihara, 1974; Özdemir, 2006; Alagöz et al., 2012), almost complex and almost quaternionic structures have been investigated widely. These structures are special structures on the tangent bundle of a manifold. A detailed review can be found in Kirichenko and Arseneva (1997). Let us recall some basic facts and definitions from literature. In this work, by a manifold, we mean a smooth manifold, that is, a Hausdorff space with a fixed complete atlas compatible with the pseudo group