论文标题
与结构组$ u（n）\ times o（s）$的歧管的共同体学
Cohomology of manifolds with structure group $U(n)\times O(s)$
论文作者
论文摘要
我们引入了一个新的光谱序列，以研究$ \ Mathcal {k} $ - 流形，该序列是通过限制Riemannian叶片的光谱序列而产生的，以在$ \ {ξ_1，...，...，ξ_s\} $的流量下形成不变性。我们使用此序列将许多定理从$ k $ -contact几何形状到$ \ MATHCAL {K} $ - 歧管。最重要的是，我们计算$ \ Mathcal {s} $的谐波圈和谐波形式 - 分别（分别是原始的基本同谋和原始基本谐波形式）（分别）。作为此的直接结果，我们得到$ \ Mathcal {s} $ - 歧管的基本共同体是拓扑不变的。我们还表明，$ \ Mathcal {S} $ - 歧管的基本Hodge数字在变形下是不变的。最后，我们为$ \ Mathcal {C} $ - 歧管提供了类似的结果。
We introduce a new spectral sequence for the study of $\mathcal{K}$-manifolds which arises by restricting the spectral sequence of a Riemannian foliation to forms invariant under the flows of $\{ξ_1,...,ξ_s\}$. We use this sequence to generalize a number of theorems from $K$-contact geometry to $\mathcal{K}$-manifolds. Most importantly we compute the cohomology ring and harmonic forms of $\mathcal{S}$-manifolds in terms of primitive basic cohomology and primitive basic harmonic forms (respectively). As an immediate consequence of this we get that the basic cohomology of $\mathcal{S}$-manifolds are a topological invariant. We also show that the basic Hodge numbers of $\mathcal{S}$-manifolds are invariant under deformations. Finally, we provide similar results for $\mathcal{C}$-manifolds.
