Tenseness of Riemannian flows

Nozawa, Hiraku; Prieto, José Ignacio Royo

doi:10.5802/aif.2885

Cited by 4 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The second author [No12] generalized their results for complete Riemannian foliations whose space of leaf closures is compact. The case of Riemannian foliations of dimension one was established by the second author and Royo Prieto [NRP12]. A part of these works is summarized as follows.…”

Section: ˆ(Fη)mentioning

confidence: 99%

Localization of Chern–Simons type invariants of Riemannian foliations

2017

Self Cite

View full text Add to dashboard Cite

show abstract

Section: ˆ(Fη)mentioning

confidence: 99%

Localization of Chern–Simons type invariants of Riemannian foliations

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…We say that μ is tense if its mean curvature form is basic. We shall say that a tense metric μ is strongly tense if κ μ is also closed (see [19,Def. 2.4]; in [22] and [23] it is called a D-metric).…”

Section: Differential Formsmentioning

confidence: 99%

Cohomological tautness of singular Riemannian foliations

Prieto

Saralegi-Aranguren

Wolak

2018

RACSAM

Self Cite

View full text Add to dashboard Cite

For a Riemannian foliation F on a compact manifold M, J. A. Álvarez López proved that the geometrical tautness of F , that is, the existence of a Riemannian metric making all the leaves minimal submanifolds of M, can be characterized by the vanishing of a basic cohomology class κ M ∈ H 1 (M/F) (the Álvarez class). In this work we generalize this result to the case of a singular Riemannian foliation K on a compact manifold X. In the singular case, no bundlelike metric on X can make all the leaves of K minimal. In this work, we prove that the Álvarez classes of the strata can be glued in a unique global Álvarez class κ X ∈ H 1 (X /K). As a corollary, if X is simply connected, then the restriction of K to each stratum is geometrically taut, thus generalizing a celebrated result of E. Ghys for the regular case.

show abstract

“…Remark 2. A fundamental property of κ b is that it is a closed differential basic form, the corresponding basic cohomology class being denoted by ξ(F ); this cohomology class (called Álvarez class [14,15]) is independent on the metric g.…”

Section: Preliminariesmentioning

confidence: 99%

A note on transverse divergence and taut Riemannian foliations

Slesar

2015

Journal of Geometry and Physics

View full text Add to dashboard Cite

In this note we give a characterization of taut Riemannian foliations using the transverse divergence. This result turns out to be a convenient tool in the case of some standard examples. Furthermore, we show that a classical tautness result of Haefliger can be obtained in our particular setting as a straightforward consequence. In the final part of the paper we obtain a tautness characterization for transversally oriented foliations with dense leaves and investigate the case of a submanifold of lower dimension which is closed and orthogonal to the leaves.Comment: 13 pages, as accepted for publication in J Geom Phy

show abstract

Tenseness of Riemannian flows

Cited by 4 publications

References 11 publications

Localization of Chern–Simons type invariants of Riemannian foliations

Localization of Chern–Simons type invariants of Riemannian foliations

Cohomological tautness of singular Riemannian foliations

A note on transverse divergence and taut Riemannian foliations

Contact Info

Product

Resources

About