On almost contact manifolds admitting axiom of planes or axiom of free mobility

A Riemannian manifold is said to admit the axiom of planes if there exists a 2-dimensional totally geodesic submanifold tangent to any 2-dimensional section at every point of the manifold, and is said to admit the free mobility if there exists an isometry which carries any point and any frame attached to the point to any other point and any other frame attached to the point [1]. It is well known that a Riemannian manifold admits the axiom of planes or the free mobility if and only if it is of constant curvature [1]. Yano and Mogi [8] proved a similar result in a complex manifold. If the holomorphic sectional curvature at every point of a Kahler manifold does not depend on the holomorphic section at the point, then it is constant on the manifold and the curvature tensor has the form