Abstract
AbstractWe introduce a new spectral sequence for the study of $${\mathcal {K}}$$
K
-manifolds which arises by restricting the spectral sequence of a Riemannian foliation to forms invariant under the flows of $$\{\xi _1,\ldots ,\xi _s\}$$
{
ξ
1
,
…
,
ξ
s
}
. We use this sequence to generalize a number of theorems from K-contact geometry to $${\mathcal {K}}$$
K
-manifolds. Most importantly we compute the cohomology ring and harmonic forms of $${\mathcal {S}}$$
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 $${\mathcal {S}}$$
S
-manifolds are a topological invariant. We also show that the basic Hodge numbers of $${\mathcal {S}}$$
S
-manifolds are invariant under deformations. Finally, we provide similar results for $${\mathcal {C}}$$
C
-manifolds.
Publisher
Springer Science and Business Media LLC
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