p,there is X∈ XF with X(p) = v. (2) Every geodesic that is perpendicular at one point to a leaf is horizontal, i.e., is perpendicular to every leaf it meets. A leaf Lof F (and each point in L) is called regular if the dimension of Lis maximal, otherwise Lis called singular. SRFs were defined by Molino [41] in his study of Riemannian ...

There is a rich and detailed theory of Riemannian foliations (M, F, g) due to Molino [36] and further developed by several authors (see also, for example, the references [45], [26], [35]); we survey parts of this theory in Section 2. ... We give a brief overview of Molino's theory [36] and discuss transfer of basic vector bundles to the Molino ...

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 ...

Molino's description of Riemannian foliations on compact manifolds extends to compact equicontinuous foliated spaces as developed by Àlvarez Lòpez and …

Book Title: Riemannian Foliations. Authors: Pierre Molino. Series Title: Progress in Mathematics. DOI: https://doi/10.1007/978-1-4684-8670-4. Publisher: Birkhäuser …

Regular Riemannian foliations are relatively well known and have a robust structural theory, due mainly to Molino [].This theory establishes that the leaf closures of such a foliation ({{mathcal {F}}}) form a singular Riemannian foliation (overline{{{mathcal {F}}}}), which moreover is described by the action of a locally …

Riemannian foliations occupy an important place in geometry. An excellent survey is A. Haefliger's Bourbaki seminar [11], and the book of P. Molino [18] is the standard ref-erence for Riemannian foliations. In one of the appendices to this book, E. Ghys proposes the problem of developing a theory of equicontinuous foliated spaces paralleling ...

The theory of P. Molino (1986) gives a homeomorphism between the leaf closure space of a Riemannian foliation and the basic manifold; the results of this paper show that the metric on the basic manifold may be chosen so that the homeomorphism preserves the transverse geometry and transfers the basic analysis to invariant analysis.

Cite this chapter. Molino, P. (1988). Elements of Foliation Theory. In: Riemannian Foliations. Progress in Mathematics, vol 73.

P. Molino, Riemannian Foliations, Progr. Math., Birkhäuser, 1988. [4] R. Wolak, Basic cohomology for singular Riemannian foliations, Monatsh. Math. 128 (1999) 159â€"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.

by Molino. View More. Paperback (Softcover reprint of the original 1st ed. 1988) $129.99 . Paperback (Softcover reprint of the original 1st ... the universal covering of the leaves.- 3.6. Riemannian foliations with compact leaves and Satake manifolds.- 3.7. Riemannian foliations defined by suspension.- 3.8. Exercises.- 4 Transversally ...

foliated manifold equipped with a bundle-like metric is called Riemannian foliation. Molino's the-ory [16] is a mathematical tool for studying Riemannian foliations. Roughly, to each transversely oriented Riemannian foliation (M,F) of codimension q, Molino associated an oriented manifold W equipped with an action of the orthogonal group SO(q ...

Preliminaries In this section, for the convenience of the reader, we will recall some basic definitions and results. The only new result of this section is Proposition 2. 1.1. Totally geodesic foliations A foliation on a complete Riemannian manifold (M, g) is called totally geodesic if its leaves are totally geodesic submanifolds of (M, g).

Pierre Molino. Chapter. 743 Accesses. 16 Citations. Part of the book series: Progress in Mathematics ( (PM,volume 73)) Abstract. The global geometry of Riemannian foliations …

structure theorems of P. Molino for Riemannian foliations [Mo] its proof is reduced to the case of Lie foliations, where it is a consequence of the main. result of this paper (?3): …

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 ...

Molino, Pierre Published: Boston, MA : Birkhäuser Boston, 1988. Physical Description: XII, 344 pages : online resource ... the universal covering of the leaves -- 3.6. Riemannian foliations with compact leaves and Satake manifolds -- 3.7. Riemannian foliations defined by suspension -- 3.8. Exercises -- 4 Transversally Parallelizable 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 ...

Using a new type of Jacobi field estimate we will prove a duality theorem for singular Riemannian foliations in complete manifolds of nonnegative sectional curvature. ... Riemannian Foliations. P. Molino G. Cairns. Mathematics. 1988; 695. PDF. 1 Excerpt; Save. Related Papers. Showing 1 through 3 of 0 Related Papers. 88 Citations; 10 …

W e are going to work in the framework of the singular riemannian foliations introduced by Molino. 1.1 The SRF. A singular riemannian foliation (SRF for short) on a manifold M is a partition.

We study relations between certain totally geodesic foliations of a closed flat manifold and its collapsed Gromov–Hausdorff limits. Our main results explicitly identify such collapsed limits as flat orbifolds, and provide algebraic and geometric criteria to determine whether they are singular.

Riemannian Foliations. P. Molino, G. Cairns. Published 1988. Mathematics. View via Publisher. link.springer. Save to Library. Create Alert. Cite. 688 Citations. Citation …

Presentation of the singular riemannian foliations1 1 We are going to work in the framework of the singular riemannian foliations introduced by Molino. 1.1 The SRF. A singular riemannian foliation (SRF for short) on a manifold M is a partition F by connected immersed submanifolds, called leaves, verifying the following properties: I- The module ...

Cite this chapter. Molino, P. (1988). Basic Properties of Riemannian Foliations. In: Riemannian Foliations. Progress in Mathematics, vol 73.

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 ...

Due to the theorem about structure of leaves by P.Molino, ... which can help the readers to form basic concepts about Riemannian foliations, for example Theorem 2.2.2, Proposition 2.2.4.

Finiteness and tenseness theorems for Riemannian foliations. D. Domínguez. Mathematics. 1998; We prove a finiteness theorem for ... P. Molino. Mathematics. 1982; 90. Save. Chapter 2 Foliations. Raymond. Barre A ... We study framed foliations such that the framing of the normal bundle can be chosen to be invariant under the linear holonomy of ...

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. As a corollary, we deduce vanishing and finiteness theorems for Riemannian foliations without assuming the harmonicity of the …

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

Using the above Riemannian vector bundles isometry and applying (6) for Θ h − 1 ω, we obtain the formula (8) 〈 Δ h ω, ω 〉 = 〈 ∇ h ω, ∇ h ω 〉 + 〈 K h ω, ω 〉, where the inner product is obtained integrating on the closed Riemannian manifold M (see e.g. [4] ). We will express all terms of (8) as polynomials in h.