论文标题
$ k $ - 倾斜分布
$k$-slant distributions
论文作者
论文摘要
受到倾斜分布和倾斜的submanifold的概念的启发，以及它们的变体，半倾斜，半浮标，两次或几乎是双人的，我们介绍了$ k $ slant的分布和$ k $ k $ slant submanifold的更一般概念，几乎是荒谬的，几乎是一个介绍，几乎是riemann antrric and ri antrric and ri antric andrric andrric andrric，他们的特性。我们证明，对于任何适当的$ k $ slant分布，在riemannian歧管的切线捆绑包中，其正交补体中存在另一个，我们建立了基本关系（公制属性，相关的张量领域的公式，共同属性，共同属性）。此外，允许倾斜角度取决于歧管的点，我们将这些概念和倾斜分布的倾斜分布和倾斜的倾斜度submanifold推广到上述设置中的$ k $ point Copointiscoptiscoptisconcopt Chub倾斜分布和$ k $ k $ pointSisce的倾斜submanifold。对于任何$ k $ - 点的倾斜分布，我们证明其正交补体中存在相应的分布，并揭示它们之间的基本关系。我们还为$ k $ pointwise的倾斜分布提供了足够的条件，以成为$ k $ slant分布并建立其他相关的结果。到最后，为了满足某些特定要求，我们引入了特殊的$ k $ pointiswise倾斜分布，即$ k $ slant发行版的分布以及相应的submanifolds，即$ k $ k $ slant的submanifolds，这比对ronsse seew ronsse的一系列通用的submanifolds类别更一般。
Inspired by the concepts of slant distribution and slant submanifold, with their variants of hemi-slant, semi-slant, bi-slant, or almost bi-slant, we introduce the more general concepts of $k$-slant distribution and $k$-slant submanifold in the settings of an almost Hermitian, an almost product Riemannian, an almost contact metric, and an almost paracontact metric manifold and study some of their properties. We prove that, for any proper $k$-slant distribution in the tangent bundle of a Riemannian manifold, there exists another one in its orthogonal complement, and we establish basic relations (metric properties, formulae relating the involved tensor fields, conformal properties) between them. Furthermore, allowing the slant angles to depend on the points of the manifold, we generalize these concepts and those of pointwise slant distribution and pointwise slant submanifold to the concepts of $k$-pointwise slant distribution and $k$-pointwise slant submanifold in the above-mentioned settings. For any $k$-pointwise slant distribution, we prove the existence of a corresponding one in its orthogonal complement and reveal basic relations between them. We also provide sufficient conditions for $k$-pointwise slant distributions to become $k$-slant distributions and establish other related results. By the end, for the fulfilment of some specific requirements, we introduce a special class of $k$-pointwise slant distributions, that of pointwise $k$-slant distributions, and the corresponding class of submanifolds, pointwise $k$-slant submanifolds, which is slightly more general than the class of generic submanifolds in sense of Ronsse, getting new results.
