2022
DOI: 10.48550/arxiv.2210.03000
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On isometric immersions of almost $k$-product manifolds

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

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