We study basic curvature groups $H^\prime_B (M,\mathcal{F}, Γ)$ associated to a foliated Riemannian manifold $(M, \mathcal{F}, g)$ [generalizing Vaisman's curvature groups of a Riemannian space form; cf.[ (The curvature groups of a space form, Ann. Sc. Norm. Super. Pisa 22 (1968), 331–341.)] and their relationship to the basic cohomology groups of $(M,\mathcal{F})$. We show that H^\prime_B (M, \mathcal{F}, Γ)=0$ for any Einstein foliation $\mathcal{F}$ of non-zero transverse scalar curvature.
On the curvature groups of a Riemannian foliation
DRAGOMIR, Sorin;
2011-01-01
Abstract
We study basic curvature groups $H^\prime_B (M,\mathcal{F}, Γ)$ associated to a foliated Riemannian manifold $(M, \mathcal{F}, g)$ [generalizing Vaisman's curvature groups of a Riemannian space form; cf.[ (The curvature groups of a space form, Ann. Sc. Norm. Super. Pisa 22 (1968), 331–341.)] and their relationship to the basic cohomology groups of $(M,\mathcal{F})$. We show that H^\prime_B (M, \mathcal{F}, Γ)=0$ for any Einstein foliation $\mathcal{F}$ of non-zero transverse scalar curvature.File in questo prodotto:
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