A Note on Weinstein's Conjecture
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 ...
TOPOLOGICAL DESCRIPTION OF RIEMANNIAN …
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 ...
Singular Riemannian foliations on simply connected spaces
P. Molino, Riemannian foliations, Progress in Mathematics vol. 73, Birkhäuser Boston 1988. Jan 1988; Lect Notes Math; R S Palais; C L Terng; R.S.Palais and C.L. Terng, Critical point theory and ...
Totally geodesic Riemannian foliations with locally symmetric …
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 …
Subspace foliations and collapse of closed flat manifolds
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.
Closure of singular foliations: the proof of Molino's …
Closure of singular foliations: the proof of Molino's conjecture. Part of: Differential topology Global differential geometry Published online by Cambridge University Press: ... One of the most fundamental results in the theory of singular Riemannian foliations is the homothetic transformation lemma. A deeper discussion of this lemma, ...
SINGULAR RIEMANNIAN FOLIATIONS AND THEIR QUADRATIC …
We present a new link between the Invariant Theory of infinitesimal singular Riemannian foliations and Jordan algebras. This, together with an inhomogeneous version of Weyl's First Fundamental Theorems, provides a characterization of the recently discovered Clifford foliations in terms of basic polynomials. This link also yields new …
Singular Riemannian foliations on simply connected spaces
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 ...
Riemannian foliations and geometric quantization
Background on Riemannian foliations. In this section we recall various definitions and results in the theory of Riemannian foliations that we shall need in later sections. We give a brief overview of Molino's theory [36] and discuss transfer of basic vector bundles to the Molino manifold. 2.1. Riemannian foliations
Riemannian Foliations [electronic resource] / by Pierre Molino
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 ...
arXiv:2105.07549v2 [math.DG] 10 Jun 2021
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 …
Cohomology of singular Riemannian foliations
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.
Ken Richardson's Publications and Preprints
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.
Singular Riemannian Foliations | SpringerLink
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 …
Mean Curvature of Riemannian Foliations | Canadian …
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 …
Riemannian Foliations | Semantic Scholar
Riemannian Foliations. P. Molino, G. Cairns. Published 1988. Mathematics. View via Publisher. link.springer. Save to Library. Create Alert. Cite. 688 Citations. Citation …
EQUIVARIANT BASIC COHOMOLOGY OF …
Regular Riemannian foliations are relatively well known and have a robust structural theory, due mainly to P. Molino [21]. This theory establishes that the leaf closures of …
arXiv:1203.6829v1 [math.DG] 30 Mar 2012
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 ...
arXiv:2006.03164v3 [math.DG] 3 Oct 2022
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
A Decomposition Theorem for the Spectral …
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): …
Riemannian Foliations (Progress in Mathematics): Molino: …
Riemannian Foliations (Progress in Mathematics) Softcover reprint of the original 1st ed. 1988 Edition. by Molino (Author) See all formats and editions. 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 ...
Foliations with Leaf Structures | Journal of Mathematical …
T. Inaba, The tangentially a.ne structure of Lagrangian foliations and the tangentially projective structure of Legendrian foliations, Preprint. T. Inaba and K. Masuda, "Tangentially affine foliations and leafwise affine functions on the torus," Kodai Math. J., 16, No. 1, 32-43 (1993).
Equivariant basic cohomology of singular Riemannian foliations
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 …
Elements of Foliation Theory | SpringerLink
Cite this chapter. Molino, P. (1988). Elements of Foliation Theory. In: Riemannian Foliations. Progress in Mathematics, vol 73.
Singular Riemannian foliations on simply connected …
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 …
Leaf closures of Riemannian foliations: A survey on …
The main goal of this article is to survey the classical theory of Riemannian and Killing foliations, including Molino's structural theory and the pseudogroup …
Weitzenböck formulas for Riemannian foliations
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.
Geometric resolution of singular Riemannian foliations
All results are proven in the more general case of singular Riemannian foliations. We prove that an isometric action of a Lie group on a Riemannian manifold admits a resolution preserving the transverse geometry if and only if the action . ... Molino P.: Riemannian Foliations. Birkhäuser Boston, Inc, Boston (1988)
Foliated vector bundles and Riemannian foliations
P. Molino, Riemannian Foliations, Progress in Mathematics, vol. 73, Birhäuser, Boston, 1988. [6] M. Popescu, P. Popescu, Lagrangians adapted to submersions and foliations, Differential Geometry and its Applications 27 (2) (2009) 171â€"178. [7] Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer …
(PDF) Top-Dimensional Group of the Basic Intersection
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.