In memorial of Connor Lazarov, 1937 – 2003 Born – September 26, 1937 Died – February 27, 2003 ConnorwastheonlychildofJulianandMildredLazarov,
We are motivated by a conjecture of Anosov: for a generic holomorphic foliation on ({mathbb {P}}^2), all but countably many leaves are disks (see e.g. Ilyashenko ). Our main concern is holomorphic foliations on ({mathbb {P}}^k). Generically, such a foliation does not admit a non-trivial directed image of the complex plane, and in ...
We describe the space of measured foliations induced on a compact Riemann surface by meromorphic quadratic differentials. We prove that any such foliation is realized by a unique such differential q if we prescribe, in addition, the principal parts of $$sqrt{q}$$ q at the poles. This generalizes a theorem of Hubbard and Masur for holomorphic quadratic …
Espaces diffeologiques quotients de feuilletages et geometrie en dimension infinie, G. Hector leafwise reduced cohomology and subfoliations, J. Alvarez Lopez transverse index theory, S. Hurder index theory for Riemannian foliations, F.W. Kamber geometry of Lagrangian foliations and integrable Hamiltonian systems, P. Molino on …
Molino's description of Riemannian foliations on compact manifolds is generalized to the setting of compact equicontinuous foliated spaces, in the case where the leaves are …
P. Molino, Riemannian foliations. Progress in Mathematics 73. Birkhäuser Boston, Inc., Boston, MA, 1988. Münzner H.F.: Isoparametrische Hyperflächen in Sphären. ... An extended version of a talk given at the international workshop Riemann International School of Mathematics held in Verbania, Italy, April 19-24, 2009. Rights and permissions ...
Let Σ be the section of F that contains p and define Σ ˜: = π −1 (Σ). Let ρ: E → E / F ˜ be the natural projection. Since the regular leaves of F ˜ are compact and have trivial holonomy (see Molino [6, Proposition 3.7, p. 94]), we have the following claim: Claim 5.1. ρ: Σ ˜ r → E r / F ˜ is a covering map, where Σ ˜ r = Σ ...
Aiming at a broad audience, in this survey we introduce Killing foliations from the very basics, starting with a brief revision of the main objects appearing in this theory, such as pseudogroups, sheaves, holonomy and basic cohomology. We then review Molino's structural theory for Riemannian foliations and present its transverse …
J Geom Anal (2020) 30:2593–2614 https://doi/10.1007/s12220-017-9975-0 Topology and Complex Structures of Leaves of Foliations by Riemann Surfaces Nessim Sibony1 ...
on the parameter f ; Vol(M) is the volume of (M,g).Ifthere is a point p in M with f (p) = 1 then the constant C can be written C = m i=1 n i G(a i, p). Theorem 1 has a direct application to principal circle bundles over closed Riemann surfaces. Let : P → M be a principal circle bundle over a closed Rie-mann surface.
Authors and Affiliations. Institut de Mathématiques, Université des Sciences et Techniques du Languedoc, 34060, Montpellier Cedex, France. Pierre Molino
The needed basic concepts from foliation theory can be seen in [14, 33, 34].Let ({mathcal F}) be a (smooth) foliation of codimension q on a manifold M.Let (T{mathcal F}subset TM) denote the vector subbundle of vectors tangent to the leaves, and (N{mathcal F}=TM/T{mathcal F}) its normal bundle. Recall that there is a natural flat leafwise partial …
On the Canonical Foliation of an Indefinite Locally Conformal Kähler Manifold with a Parallel Lee Form. We study the semi-Riemannian geometry of the foliation F of an indefinite locally conformal Kähler (l.c.K.) manifold M, given by the Pfaffian equation ω=0, provided that ∇ω=0 and c=∥ω∥≠0 (ω is the….
S.P.Novikov1 Topology of Foliations given by the real part of holomorphic 1-forms Abstract. Topology of Foliations of the Riemann Surfaces given by the real part of generic holomorphic 1-forms, is studied. Our approach is based on the notion of Transversal Canonical Basis of Cycles (TCB) instead of
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 ...
Riemannian Foliations [electronic resource] / by Pierre Molino. Author: Molino, Pierre. Published: Boston, MA : Birkhäuser Boston, 1988. Physical Description: XII, 344 pages : …
Riemannian foliations with compact leaves and Satake manifolds.- 3.7. Riemannian foliations defined by suspension.- 3.8. Exercises.- 4 Transversally Parallelizable Foliations.- 4.1. The basic fibration.- 4.2. CompIete Lie foliations.- 4.3. The structure of transversally parallelizable foliations.- 4.4. The commuting sheaf C(M, F).- 4.5.
Lineation occurs when amphiboles, kyanite, sillimanite, and other minerals that form long thin crystals, lie parallel in a rock. The photo below in Figure 8.24 shows lineation caused by aligned hornblende (amphibole) crystals. Figure 8.24: Aligned crystals of black hornblende give this rock lineation. The crystals are up to 2 cm long.
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Riemannian foliations occupy an important place in geometry. An excellent survey is A. Haefliger's Bourbaki seminar [6], and the book of P. Molino [13] is the standard refer . Read More P. Molino Semantic Scholar. Semantic Scholar profile for P. Molino, with 122 highly influential citations and 18 scientific research papers.
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 …
Ifone writes he corresponding equations for the lengths in Figure 2, one gets li +16 =11+12+13+14. 14+ 15ffi l~+ 18+ 15+ le. This system hasno positive solutions. Of course, there are quivalent metric foliations which are induced by quadratic forms; for instance that obtained bycollapsing l~and 13to points.
The same strategy can be applied to general Riemannian foliations by using Molino's theory [22] and more specifically the following important result: Molino's Structure Theorem. If F is a smooth Riemannian foliation of a compact connected manifold, then F lifts to a smooth foliation F T on the transverse orthonormal frame bundle E T of F ...
The conditions studied in this paper are closely related to [4, 5, 10, 12] and they have initially the origin in a special case of a problem presented by E. Ghys in Appendix E of P. Molino's book ...
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.
It follows that the Riemannian metric in Q ( Q) defined by 〈 w 1, w 2 〉 = 〈 θ −1 ( w 1), θ −1 ( w 2) 〉 for all w 1, w 2 ∈ H, 〈 v, w 〉 = 0 for all v ∈ V, w ∈ H is a …
There is a rich structural theory for Riemannian foliations, due mainly to P. Molino, that asserts, among other results, that a complete Riemannian foliation F admits a locally constant sheaf C F of Lie algebras of germs of local transverse Killing vector fields whose action describes the dynamics of F, in the sense that for each leaf L x ∈ F ...
About this book. Foliation theory has its origins in the global analysis of solutions of ordinary differential equations: on an n-dimensional manifold M, an [autonomous] differential …
38, p. 217–255. Enseignement Math., Geneva, 2001 MR2003k:58042; ... Algebraic foliations and derived geometry: the Riemann-Hilbert correspondence, (arXiv:2001.05450) Last revised on June 8, 2024 at 13:13:16. See the history of this page for a list of all contributions to it.
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 singularities, then its trajectories form a par tition of M into curves, i.e. a foliation of codimension n - 1.
