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- José Ignacio Royo Prieto, Robert Wolak
- 2005

For a riemannian foliation F on a closed manifold M , it is known that F is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form κ µ (relatively to a suitable riemannian metric µ) is zero (cf. [1]). In the transversally orientable case, tautness is equivalent to the non-vanishing of the top… (More)

- Robert A Wolak
- 1996

In recent years the graph of a foliation, an object which has been known for a long time, cf. 10], has known new interest. In fact there are two groupoids associated with a foliation, the homotopy groupoid and the holonomy groupoid, sometimes called the graph. It serves as a basis for the construction of the C-algebra associated to the foliation. Moreover,… (More)

- Robert Wolak
- 2008

In the paper we introduce the notions of a singular fibration and a singular Seifert fi-bration. These notions are natural generalizations of the notion of a locally trivial fibration to the category of stratified pseudomanifolds. For singular foliations defined by such fibra-tions we prove a de Rham type theorem for the basic intersection cohomology… (More)

- Martintxo Saralegi-Aranguren, Robert Wolak
- 2005

We study the cohomology properties of the singular foliation F determined by an action Φ : G× (M, µ) → (M, µ) where the abelian Lie group G preserves the riemannien metric µ on the compact manifold M. More precisely, we prove that the basic intersection cohomology IH * p (M/F) is finite dimensional and verifies the Poincaré Duality. This duality includes… (More)

A family of probability distributions parametrized by an open domain Λ in R n defines the Fisher information matrix on this domain which is positive semi-definite. In information geometry the standard assumption has been that the Fisher information matrix is positive definite defining in this way a Riemannian metric on Λ. If we replace the "positive… (More)

- José Ignacio Royo Prieto, Robert Wolak
- 2005

It is known that, for a regular riemannian foliation on a compact manifold, the properties of its basic cohomology (non-vanishing of the top-dimensional group and Poincaré duality) and the tautness of the foliation are closely related. If we consider singular riemannian foliations, there is little or no relation between these properties. We present an… (More)

- Jerzy J. Konderak, Robert A. Wolak, Jerzy J. KONDERAK, Robert A. WOLAK
- 2002

We consider leaf preserving maps between manifolds equipped with Riemannian foliations. We construct a transversal tension field for such maps and define transversally harmonic maps. Then we give some examples of such maps using the suspension construction.

- Martintxo Saralegi-Aranguren, Robert Wolak
- 2012

We prove that the basic intersection cohomology I H * p (M/F), where F is the singular foliation determined by an isometric action of a Lie group G on the compact manifold M, is finite dimensional. This paper deals with an action Φ : G × M → M of a Lie group on a compact manifold preserving a riemannian metric on it. The orbits of this action define a… (More)

- José Ignacio Royo Prieto, Robert Wolak
- 2008

To Nicolae Teleman on his 65th birthday. Abstract In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological… (More)