Slant submersions from almost product Riemannian manifolds (Q2862264)

Let \(\pi\) be a \(C^\infty\)-submersion from a Riemannian manifold \((M,g)\) onto a Riemannian manifold \((B,g')\). It is known that there are several kinds of submersions defined by certain conditions. Consequently, for each of these submersions one can study the corresponding geometry and its applications. In this spirit the author, firstly, introduces the notion of almost product Riemannian submersions. He proves that if \(M\) is a locally product Riemannian manifold then \(B\) is also a locally product manifold. Next, he defines slant Riemannian submersions, gives examples, and studies the geometry of leaves of the distributions. He obtains also necessary and sufficient conditions for a slant submersion to be totally geodesic.