On isometric immersions of almost k-product manifolds

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 to geometry, special part also related geometry Our contains type B.-Y Chen's δ-invariants. Applications are given for isometric immersions multiply twisted warped products (we improve some known inequalities by replacing sectional our invariant) problems non-immersion non-existence compact leaves foliated submanifolds.