Leaf closures of Riemannian foliations: A survey on
2022.6.1 Molino theory consists of a structural theory for Riemannian foliations developed by P. Molino and others in the decade of 1980. In this section we summarize
Read More
Riemannian Foliations Semantic Scholar
Riemannian Foliations @inproceedings {Molino1988RiemannianF, title= {Riemannian Foliations}, author= {Pierre. Molino and Grant Cairns}, year= {1988} } P. Molino, G.
Read More
arXiv:2006.03164v1 [math.DG] 4 Jun 2020
2021.11.21 There is a rich structural theory for Riemannian foliations, due mainly to P. Molino, that
Read More
A generalization of Molino's theory and equivariant basic Â
2021.5.17 Abstract: Molino's theory is a mathematical tool for studying Riemannian foliations. In this paper, we propose a generalization of Molino's theory with two
Read More
Structure of Riemannian Foliations SpringerLink
For Riemannian foliations on closed manifolds, Molino has found a remarkable structure theorem [Mo 8,10]. This theorem is based on several fundamental observations.
Read More
Singular Riemannian foliations on simply connected spaces
2006.7.1 Typical examples of singular Riemannian foliations with sections are the set of orbits of a polar action, parallel submanifolds of an isoparametric submanifold in a
Read More
Leaf closures of Riemannian foliations: A survey on
2022.6.1 Molino theory consists of a structural theory for Riemannian foliations developed by P. Molino and others in the decade of 1980. In this section we summarize
Read More
Foliations - Texas Christian University
2018.7.30 topological obstructions. For instance, in Riemannian foliations, the leaf closures partition the manifold and are in particular disjoint. This does not happen in Example 1.5, so the Reeb-type foliation is not Riemannian. However, the other four examples in the previous section are Riemannian foliations in the obvious metrics.
Read More
Liouville type theorem for (F;F')p-harmonic maps on foliations
P. Molino, Riemannian foliations, translated from the French by Grant Cairns, Boston: Birkhäser, 1988. Calculus of Variations and Partial Differential Equations. Request PDF Liouville type ...
Read More
Singular Riemannian foliations on simply connected spaces
2006.7.1 We start by recalling the definition of a singular Riemannian foliation (see the book of P. Molino [6]). Definition 1.1. A partition F of a complete Riemannian manifold M by connected immersed submanifolds (the leaves) is called a singular foliation of M if it verifies condition (1) and singular Riemannian foliation if it verifies conditions (1 ...
Read More
Unique ergodicity of the horocycle flow on Riemannnian foliations
In this paper, we prove that for the special case of Riemannian foliations, strict ergodicity of the horocycle flow still holds. This, in particular, proves that this flow is minimal, which establishes a conjecture proposed by Matsumoto. The main tool is a theorem due to Coudène, which he presented as an alternative proof for the surface case ...
Read More
Cohomology of singular Riemannian foliations - ScienceDirect
2006.4.15 P. Molino, Riemannian Foliations, Progr. Math., Birkhäuser, 1988. [4] R. Wolak, Basic cohomology for singular Riemannian foliations, Monatsh. Math. 128 (1999) 159–163. nrightbig for an open set U ⊂ M/ overbar F. It is the derived sheaf ofA t F . With the differential induced by d,H q (p,A ∗ F ) is a differential sheaf.
Read More
On the horizontal diameter of the unit sphere Archiv der
2017.11.21 For a singular Riemannian foliation $$\\mathcal {F}$$ F on a Riemannian manifold M, a curve is called horizontal if it meets the leaves of $$\\mathcal {F}$$ F perpendicularly. For a singular Riemannian foliation $$\\mathcal {F}$$ F on a unit sphere $$\\mathbb {S}^{n}$$ S n , we show that if $$\\mathcal {F}$$ F satisfies some properties,
Read More
Finiteness and tenseness theorems for Riemannian foliations
1998.12.1 Tondeur, Foliations and metrics, Progr. Math. , vol. 32, 1983, pp. 103-152]). We also show that the main tautness theorems for Riemannian foliations on compact manifolds, which were proved by several authors, are
Read More
The Structure of Lorentzian Foliations of Codimension Two
2020.12.25 At present Riemannian foliations are the best investigated class of foliations (P. Molino [], A. Haefliger [], F. Tondeur [] and others).R. Wolak [] raised the question of finding the conditions under which a foliation is Riemannian and proved that a complete G-foliation all of whose leaves are compact is Riemannian.Criteria and other
Read More
Singular Riemannian Foliations SpringerLink
Cite this chapter. Molino, P. (1988). Singular Riemannian Foliations. In: Riemannian Foliations. Progress in Mathematics, vol 73.
Read More
Mean Curvature of Riemannian Foliations Canadian
However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button. It is shown that a suitable conformai change of the metric in the leaf direction of a transversally oriented Riemannian foliation on a closed manifold will make the basic component of the mean curvature harmonic.
Read More
arXiv:2006.03164v3 [math.DG] 3 Oct 2022
2022.10.5 There is a rich structural theory for Riemannian foliations, due mainly to P. Molino, that ... Riemannian foliations which are complete an whose Molino sheaf C is globally contant. In other words, for a Killing foliation Fthere exists transverse Killing vector fields X 1;:::;X d
Read More
Foliations, submanifolds, and mixed curvature Journal of
K. Abe, “Application of a Riccati type differential equation to Riemannian manifolds with totally geodesic distributions,” Tohoku Math. J., 25, 425–444 (1973). MATH MathSciNet Google Scholar. K. Abe, “Some remarks on a class of submanifolds in space of nonnegative curvature,” Math. Ann., 247, 275–278 (1980). Article MATH MathSciNet ...
Read More
(PDF) Geometry of Foliated Manifolds - ResearchGate
2016.12.31 Abstract. In this paper some results of the authors on geometry of foliated manifolds are stated and results on geometry of Riemannian (metric) foliations are discussed. 25+ million members. 160 ...
Read More
Foliated g-structures and riemannian foliations - Springer
P. Molino, Feuilletages riemanniens sur les variétés compactes: champs de Killing transverse,C. R. Acad. Sc. Paris 289 (1979), 421–423. MATH MathSciNet Google Scholar P. Molino, Feuilletages de Lie à feuilles denses,Séminaire de Géométrie Différentielle 1982–83, Montpellier
Read More
Structure of Riemannian Foliations SpringerLink
For Riemannian foliations on closed manifolds, Molino has found a remarkable structure theorem [Mo 8,10]. This theorem is based on several fundamental observations. The first is that the canonical lift \ (\hat {\mathcal {F}}\) of a Riemannian foliation F to the bundle \ (\hat {M}\) of orthonormal frames of Q is a transversally parallelizable ...
Read More
A Note on Weinstein's Conjecture - JSTOR
foliation F, ie., that F is a Riemannian foliation with a bundle-like transverse metric in the sense of Rienhart. We refer to the excellent book of Molino [3]. For each vector field V on S, let V be the normal field to F such that V(x) is the projection on the subspace of T0S orthogonal to X,(x). Monna [5] defines a transverse metric - by the ...
Read More
Riemannian Foliations - Molino - Google Books
2012.12.6 Riemannian Foliations. Molino. Springer Science Business Media, Dec 6, 2012 - Mathematics - 344 pages. Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential equation is defined by a vector field X ; if this vector field has no ...
Read More
arXiv:1608.03552v2 [math.DG] 31 Jan 2017
2017.2.2 CLOSURE OF SINGULAR FOLIATIONS: THE PROOF OF MOLINO’S CONJECTURE MARCOS M. ALEXANDRINO AND MARCO RADESCHI Abstract. In this paper we prove the conjecture of Molino that for every singular Riemannian foliation (M,F), the partition F given by the closures of the leaves of F is again a singular Riemannian
Read More
Totally geodesic Riemannian foliations with locally symmetric
2006.3.15 Our main result is the following: Theorem 1. Let (M,F ) be a foliated manifold with a finite volume complete bundle-like Riemannian metric h for which F is totally geodesic and the leaves are isometrically covered by X G . In particular, F is a totally geodesic Riemannian foliation. If M has a dense leaf, then, up to a finite covering, F has
Read More
Duality and minimality in Reimannian foliations - Semantic
1992.12.1 For general Riemannian foliations, spectral asymptotics of the Laplacian is studied when the metric on the ambient manifold is blown up in directions normal to the leaves ... Riemannian Foliations. P. Molino G. Cairns. Mathematics. 1988; 686. PDF. Save. Sucesión espectral asociada a foliaciones riemannianas.
Read More
arXiv:2006.03164v1 [math.DG] 4 Jun 2020
2021.11.21 We then review Molino’s structural theory for Riemannian foliations and present its transverse counterpart in the theory of complete pseudogroups of isometries, emphasizing the connections between these topics. We also survey some classical ... There is a rich structural theory for Riemannian foliations, due mainly to P. Molino, that
Read More
De Rham cohomology of diffeological spaces and foliations
2011.8.1 Lie foliations. Lie foliations play a fundamental role in the theory of Riemannian foliations [10]. Let G be the Lie algebra of a simply connected (and connected) Lie group G. A foliation F on a closed manifold M is a G-Lie foliation if it is defined by a nonvanishing G-valued 1-form ω verifying the Maurer–Cartan equation ω + 1 2 [ω, ω] = 0.
Read More
(PDF) Geometry of Foliated Manifolds - ResearchGate
2019.10.30 shown that Riemannian submersions generate Riemannian foliations. This class of foliations plays very important role in the theory of foliations and is substantial from the point of view of geometry .
Read More
(PDF) Einstein Manifolds and Contact Geometry - ResearchGate
2000.1.2 [Mol1] P. Molino, Riemannian Foliations, Progress in Mathematics 73, Birkh¨ auser, Boston, 1988. [Mol2] P. Molino , F euilletages riemanniens sur les vari ´ et´ es compactes; champs de Killing ...
Read More
arXiv:2007.01325v1 [math.DG] 2 Jul 2020
2020.7.6 mannian manifolds is a submetry if and only if P is a C1 Riemannian submersion. Other large classical sources of equidistant decomposi-tions are provided by the decompositions into orbits of isometric group actions and singular Riemannian foliations with closed leaves. Singu-lar Riemannian foliations, defined by P. Molino, [Mol88],
Read More
On transversely flat conformal foliations with good
a transverse invariant Riemannian metric of (M,^) which is of class C00, namely, (Λf,^) is Riemannian in the usual sense. Thus the theory for Riemannian foliations, which can be found in Molino [3] for instance, applies for such foliations. The proof of Theorem A can be done if we simply replace the metric in the previous paper [1] with one
Read More
A generalization of Molino's theory and equivariant basic Â
2021.5.17 Molino's theory is a mathematical tool for studying Riemannian foliations. In this paper, we propose a generalization of Molino's theory with two Riemannian foliations. For this purpose, the projection of foliation with respect to a fibration is discussed. The generalization results in an equivariant basic cohomological isomorphism in case of
Read More
Introduction to foliations and Lie groupoids
2004.10.5 fibers of π is also homogeneous and the Lie foliations of the fibers are isomorphic. Thus, the Lie algebra g associated to each fiber is an invariant of F. The structure theorem of the previous paragraph is due to P. Molino [8]. Also,
Read More
arXiv:2203.15910v2 [math.DG] 31 Mar 2022
2022.4.1 ON THE TOPOLOGY OF LEAVES OF SINGULAR RIEMANNIAN FOLIATIONS 5 L 0 → Lpfrom a principal leaf L 0, whose fiber is an orbit KLvfor some principal point v∈ (νpLp,Fp), and it consists of a finite disjoint union of principal leaves of Fp. 2.3. The Molino bundle. Let (M,F) be a closed singular Riemannian foliation
Read More
A complete stability theorem for foliations with singularities
2010.8.15 From another viewpoint, there is Molino’s theory of Riemannian foliations [5] which is an important subject of current research including the study of cohomogeneity one isometric actions of Lie groups. Important applications in Differential Geometry, more specifically in Theory of Minimal Submanifolds are now notorious [3,4]. ...
Read More