This paper demostrates a method for analysing almost CR geometries (H, J), by uniquely defining a partially integrable structure (H,K) from the same data. Thus two almost CR geometries (H,J) and (H ′, J ′) are equivalent if and and only if they generate isomorphic induced partially integrable CR geometries (H,K) and (H ′, K′), and the set of CR morphisms between these spaces contains an element...

New relations involving curvature components for the various connections appearing in the theory of almost product manifolds are given and the conformal behaviour of these connections are studied. New identities for the irreducible parts of the deformation tensor are derived. Some direct physical applications in Kaluza–Klein and gauge theory are discussed. [email protected] [email protected]

A Riemannian manifold endowed with k≥2 complementary pairwise orthogonal distributions is called a almost k-product manifold. In the article, we study following problem: find relationship between intrinsic and extrinsic invariants of isometrically immersed in another For such immersions, establish an inequality that includes mixed scalar curvature square mean curvature. Although tensor belongs ...

Integral formulas are powerful tools used to obtain global results in geometry and analysis. The integral for almost multi-product manifolds, foliations multiply twisted products of Riemannian, metric-affine sub-Riemannian which this review paper is devoted, useful studying such problems as (i) the existence characterization with a given geometric property, being totally geodesic, minimal or um...