Problems of extrinsic geometry of foliations

This survey is devoted to particular problems of extrinsic geometry of foliations, which, roughly speaking, describes how leaves (or single submanifolds) are located within the ambient pseudo-Riemannian space. We discuss the following topics with the mixed scalar curvature: integral formulas and splitting of foliations, prescribing the mixed curvature of foliations, and variations of functionals defined on foliations, which seem to be central in extrinsic geometry.