Displaying similar documents to “Noncommutative spectral geometry of Riemannian foliations.”

Generalized signature operators and spectral triples for the Kronecker foliation

R. Matthes, O. Richter, G. Rudolph (2003)

Banach Center Publications

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We consider two spectral triples related to the Kronecker foliation. The corresponding generalized Dirac operators are constructed from first and second order signature operators. Furthermore, we consider the differential calculi corresponding to these spectral triples. In one case, the calculus has a description in terms of generators and relations, in the other case it is an "almost free" calculus.

On riemannian foliations with minimal leaves

Jesús A. Alvarez Lopez (1990)

Annales de l'institut Fourier

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For a Riemannian foliation, the topology of the corresponding spectral sequence is used to characterize the existence of a bundle-like metric such that the leaves are minimal submanifolds. When the codimension is ≤ 2 , a simple characterization of this geometrical property is proved.

A finiteness theorem for Riemannian submersions

Paweł G. Walczak (1992)

Annales Polonici Mathematici

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Given some geometric bounds for the base space and the fibres, there is a finite number of conjugacy classes of Riemannian submersions between compact Riemannian manifolds.