Integral volume vanishes for manifolds with circle foliations.
problem Integral foliated simplicial volume calculation.
method Regular foliation by circles analysis.
result Integral foliated simplicial volume vanishes.
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48 results for “foliated manifold”
Study on minimal foliations in 3D manifolds with specific conditions.
problem Characterizing minimal foliations in 3D manifolds.
method Analyzing Anosov foliations and their intersections.
result Necessary and sufficient conditions for orbit foliation of Anosov flows.
Simple foliated flowsmath.GT
Simple flows on manifold foliations.
problem Transversely oriented foliations on closed manifolds.
method Simple foliated flows on codimension one.
result Existence of simple foliated flows on manifolds.
Uniform foliations with Reeb components on 3-manifolds.
problem Characterizing uniform foliations with Reeb components.
method Study of foliations on 3-manifolds with infinite fundamental group.
result Examples and results on behavior of foliations.
Study of affine and projective structures on foliated complex manifolds.
problem Formalizing and analyzing affine and projective structures on foliations.
method Formalizing concepts, providing local normal forms, proving index formulae, classifying structures.
result Compact algebraic manifolds of even dimension do not admit foliated projective structures.
The paper proves a theorem about completely solvable Lie foliations on compact manifolds.
problem Generalizing Haefliger's theorem to completely solvable Lie foliations.
method Proves that every completely solvable Lie foliation on a compact manifold is the inverse image of a homogeneous foliation.
result Every completely solvable Lie foliation on a compact manifold is the inverse image of a homogeneous foliation.
Proves h-principle for symplectic foliations on closed manifolds.
problem Symplectic foliations on closed manifolds.
method Proves h-principle for regular symplectic foliations.
result Establishes h-principle for symplectic foliations on closed manifolds.
A foliation of a manifold M is called R-covered if its lift to the universal cover of M has space of leaves R. We show that there are many graph manifolds which admit taut foliations, but which do not admit any R-covered foliations. On the other hand, we show that these manifolds all have finite covers admitting R-cove…
Classifies foliations on CROSSes.
problem Classifying Riemannian foliations on CROSSes.
method Classification based on manifold homeomorphism.
result Classification of Riemannian foliations on CROSSes.
Foliations from left ordersmath.GT
Constructs foliations from manifold group left orders.
problem Creating foliations from group structures.
method Inputting a left order of a manifold's fundamental group produces a foliation.
result Establishes connections to 3D problems.
Study on transverse Ricci solitons on compact foliated manifolds.
problem Characterizing transverse Ricci solitons on compact foliated manifolds.
method Investigation of self-similar solutions of the transverse Ricci flow, analysis of taut Riemannian foliations.
result Established relations between taut Riemannian foliations and transverse Ricci solitons, found examples of transverse Ricci solitons.
Develops twistor theory for foliated manifolds, proving orbifold results.
problem Classical twistor theory applied to foliated manifolds.
method Constructs twistor space of normal bundle, proves foliated versions of results.
result Obtains orbifold versions of classical results.
Haefliger cohomology characterizes taut foliated manifolds by Haefliger's theorem. We show that Haefliger cohomology characterizes strongly tense foliated manifolds, namely, foliated manifolds which admit a Riemannian metric such that the mean curvature form of the leaves is closed and basic. We show that Haefliger coh…
The study explores conformal symplectic foliations on closed manifolds, proving their existence in dimensions 5 and above.
problem Existence of conformal symplectic foliations on closed manifolds.
method Analysis of symplectic and conformal symplectic codimension-one foliations on closed manifolds of dimension at least 5.
result Construction of conformal symplectic foliations on closed, simply-connected, almost contact manifolds in dimension 5.
Foliated Open Booksmath.GT
The paper introduces foliated open books for contact 3-manifolds with boundary foliations.
problem Studying contact manifolds with convex boundary using finer tools.
method Developed a new type of open book decomposition with a specified characteristic foliation on the boundary.
result Established the uniqueness and existence of foliated open books and their equivalence to other models.
The paper studies affine manifolds with linear foliations and their topological properties.
problem Characterizing the topology of affine manifolds with linear foliations.
method Analyzing the structure of affine manifolds and their foliations, proving topological properties.
result Compact affine manifolds with linear foliations are homeomorphic to the torus under certain conditions.
Study foliations on Riemannian manifolds with specific vector fields, focusing on geometric properties.
problem Investigate foliations transverse to closed conformal vector fields on Riemannian manifolds.
method Analyze conditions for totally geodesic leaves and geometric constraints on foliations.
result Characterize totally geodesic foliations and classify minimal and constant mean curvature foliations.
Solves generalized Kazdan-Warner equations on foliated manifolds.
problem Existence and uniqueness of solutions to generalized Kazdan-Warner equations on foliated manifolds.
method Extends theorem to compact foliated manifolds, provides examples of PDEs.
result Solves the transverse Hitchin equation and its generalizations.
The study limits the number of specific foliations with bounded geometry.
problem Bounding the number of isoparametric foliations with bounded geometry.
method Proving finitely many foliations with specific properties and constructing infinite families of non-diffeomorphic foliations.
result There are only finitely many isoparametrically foliated closed connected Riemannian manifolds with bounded geometry, up to foliated diffeomorphism.
Equation connects Ricci curvature to foliations, leading to product manifold conditions.
problem Understanding the structure of Riemannian manifolds through foliations.
method Developed an equation relating Ricci curvature to second fundamental forms of orthogonal foliations.
result Showed sufficient conditions for manifolds to be products of foliation leaves.
Study geometric properties of spacelike foliations on Lorentz manifolds.
problem Investigate conditions for spacelike foliations to be totally umbilical or geodesic.
method Develop an equation relating foliation to ambient manifold, apply Maximum principle.
result Obtain an obstruction for totally geodesic foliations in spacetimes with positive Ricci curvature.
We determine the structure of the fundamental group of the regular leaves of a closed singular Riemannian foliation on a compact, simply connected Riemannian manifold. We also study closed singular Riemannian foliations whose leaves are homeomorphic to aspherical or to Bieberbach manifolds. These foliations, which we c…
The paper solves a 5-manifold foliation problem using a Sasaki-Ricci flow.
problem Solving foliation singularities on Sasakian 5-manifolds.
method Applying the Sasaki-Ricci flow to resolve cyclic quotient foliation singularities.
result Proves a Sasaki analogue of the analytic minimal model program.
Introduces singular Finsler foliations and their properties.
problem Generalizing Finsler actions, submersions, and foliations.
method Definition and analysis of singular Finsler foliations on Randers manifolds.
result Singular Finsler foliations on Randers manifolds are singular Riemannian foliations on the Riemannian manifold induced by the metric.
Proves a Thom isomorphism for foliated differential forms.
problem Transverse Lie algebra actions on foliated manifolds and vector bundles.
method Thom isomorphism theorem for differential forms in foliated settings.
result Established a new Thom isomorphism theorem.
The article derives integral formulas for foliated sub-Riemannian manifolds.
problem Integrating geometric concepts in Riemannian manifolds with foliations.
method Deriving integral formulas involving shape operators and curvature tensor.
result Generalizes results for foliated Riemannian manifolds and includes arbitrary functions.
The paper develops theory for foliations on manifolds with boundary.
problem Analyzing the cohomology of foliated manifolds with boundary.
method Develops theory, establishes decomposition and vanishing theorems, and proves duality and extension theorems.
result Establishes Dolbeault decomposition of basic forms and proves global regularity for -equations.
Study shows codimension 2 foliations on simply-connected manifolds are smooth.
problem Existence of foliations by exotic tori on simply-connected manifolds.
method Analyzes singular Riemannian foliations on compact simply-connected manifolds.
result Foliations of codimension 2 on compact simply-connected manifolds are smooth.
3-manifolds with positive scalar curvature have controlled foliations.
problem Understanding foliations in 3-manifolds with positive scalar curvature.
method Showed a singular foliation by surfaces with controlled area and diameter.
result 3-manifolds with positive scalar curvature admit controlled foliations.
Survey on holomorphic structures on complex manifolds.
problem Holomorphic foliations with transverse holomorphic Cartan geometries.
method Analyzes G-structures and Cartan geometries on compact complex manifolds.
result Foliated holomorphic Cartan geometries on compact complex manifolds.
Study cohomology of quaternionic foliations and orbifolds.
problem Understanding cohomology of quaternionic foliations and orbifolds.
method Definition and proof of foliated versions of classical results for quaternionic Kähler manifolds.
result Formulation and proof of foliated versions of classical results for quaternionic Kähler manifolds.
Study shows how to deform foliated manifolds with flat leaves, leading to geometric characterization.
problem Deforming foliated manifolds with flat leaves while maintaining curvature bounds.
method Collapsing a manifold with a closed flat regular Riemannian foliation, keeping curvature uniformly bounded.
result For compact, simply connected manifolds, foliations are given by torus actions.
Integral foliated simplicial volume is a version of simplicial volume combining the rigidity of integral coefficients with the flexibility of measure spaces. In this article, using the language of measure equivalence of groups we prove a proportionality principle for integral foliated simplicial volume for aspherical m…
The paper proves CMC foliations for quasi-Fuchsian manifolds near the Fuchsian locus.
problem Existence of monotone CMC foliations for quasi-Fuchsian manifolds.
method Analyzes quasi-Fuchsian manifolds near the Fuchsian locus and proves the existence of a unique monotone CMC foliation.
result Proves the existence of a unique monotone CMC foliation for quasi-Fuchsian manifolds in a small neighborhood of the Fuchsian locus.
Local foliation of 3D manifolds by Willmore surfaces with curvature constraints.
problem Constructing foliations of manifolds by surfaces of Willmore type.
method Adapting a method from constant mean curvature foliations to Willmore surfaces.
result Existence of a local foliation of a 3D Riemannian manifold by Willmore critical points with area constraint.
The Hitchin-Kobayashi correspondence is extended to foliated Riemannian manifolds.
problem Proving a Hitchin-Kobayashi correspondence for foliated manifolds.
method Adapting Uhlenbeck and Yau's proof to the foliated setting, defining stability for foliated bundles, and relating to higher-dimensional instantons.
result Foliated Hermitian-Einstein connections correspond to polystability, with implications for higher-dimensional instantons.
Left orderability proven for certain 3-manifolds with specific foliations.
problem Proving left orderability for specific 3-manifolds with taut foliations.
method Analyzing the fundamental group of a 3-manifold with a co-orientable taut foliation.
result The fundamental group of the 3-manifold is left orderable.
Proves existence and uniqueness of CMC foliations in cuspidal manifolds.
problem Existence and uniqueness of CMC foliations in asymptotically cuspidal manifolds.
method Proof without curvature assumptions, applicable in any dimension.
result Proves existence and uniqueness of CMC foliations.
A K(pi,1)-foliation is one for which the universal covers of all leaves are contractible (thus all leaves are K(pi,1)'s for some pi). In the first part of the paper we show that the tangential Lusternik--Schnirelmann category cat F of a K(pi,1)-foliation F on a manifold M is bounded from below by t-codim F for any t wi…
Characterizes rigidity of compact foliations using deformations of Lie groupoids and algebroids.
problem Rigidity of compact foliations on manifolds.
method Combining stability results for foliations with recent results on deformations of Lie groupoids and Lie algebroids.
result Cohomological characterization for rigidity of compact foliations.
We give a complete classification of foliations on open contact manifolds whose leaves are contact submanifolds of the ambient manifold. The results are analogues of Haefliger's classification of foliations on open manifold.
Introduces positivity for classes in foliated manifolds.
problem Understanding positivity in foliated manifolds.
method Introduces positivity for a real basic class in basic Bott-Chern cohomology group and studies its relationship with negativity of transverse holomorphic sectional curvature.
result Establishes the relationship between positivity and negativity in foliated manifolds.
We investigate contrasting behaviours emerging when studying foliations on non-metrisable manifolds. It is shown that Kneser's pathology of a manifold foliated by a single leaf cannot occur with foliations of dimension-one. On the other hand, there are open surfaces admitting no foliations. This is derived from a quali…
3-manifolds with Heegaard 2 admit taut foliations if their fundamental group is left-orderable.
problem Characterizing 3-manifolds with taut foliations.
method Proving existence of taut foliations based on left-orderability of the fundamental group.
result 3-manifolds with Heegaard genus 2 and left-orderable fundamental group admit co-orientable taut foliations.
We study transversely Lorentzian foliations on the closed 3-manifolds. We classify them under a completeness hypothesis and we deduce the dual classification of codimension 1 geodesically complete timelike totally geodesic foliations. Besides we provide an example of a Lorentzian foliation on a compact 3-manifold which…
The study explores conditions for a manifold to be a leaf of a complete foliation on the open unit ball.
problem Conditions for a manifold to be a leaf of a complete foliation on the open unit ball.
method Analyzes conditions for manifolds to be leaves of complete foliations.
result Provides answers to the question of when a manifold can be a leaf of a complete foliation on the open unit ball.
Measuring foliations at infinity of quasi-Fuchsian manifolds, proving filling pairs and showing realisation.
problem Understanding foliations at the boundary of quasi-Fuchsian manifolds.
method Proving filling pairs and showing realisation of measured foliations.
result Proved that measured foliations at infinity of quasi-Fuchsian manifolds are filling when close to being Fuchsian.
Study numerically flat foliations on Kähler manifolds, proving new splitting theorems.
problem Understanding foliations with numerically flat tangent bundles on Kähler manifolds.
method Analyzing the structure of foliations on compact Kähler manifolds, extending earlier results.
result Smooth foliations with numerically flat tangent bundles induce a decomposition of the ambient manifold's tangent bundle.