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Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 07/2018, Volume 38, Issue 7, pp. 3223 - 3237
We study in this paper several properties concerning singularities of foliations in (C-3, 0) that are pull-back of dicritical foliations in (C-2, 0).... 
Holomorphic foliations, dicritical foliations | INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | dicritical foliations | Holomorphic foliations | DESINGULARIZATION | SINGULAR FOLIATIONS
Journal Article
2008, OXFORD MATHEMATICAL MONOGRAPHS., ISBN 0198564953
Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate relationship between Sasakian and Kähler geometries, especially... 
Contact structures | Algebraic varieties | Complex structures | Kähler geometry | Killing spinors | Orbibundles | Foliations | Orbifolds | Monge-ampère problem | Kähler-einstein metrics
Book
Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN 0075-4102, 02/2015, Volume 2015, Issue 699, pp. 1 - 33
Rational connectedness is an algebro-geometric analogue of path connectedness depending crucially on the existence of special rational curves called . For a... 
MATHEMATICS | FOLIATIONS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 11/2019, Volume 372, Issue 11, pp. 8131 - 8158
We show that a compact manifold that admits a Killing foliation with positive transverse curvature fibers over finite quotients of spheres or weighted complex... 
basic Euler characteristic | METRIC FOLIATIONS | MATHEMATICS | ORBIFOLDS | transverse symmetry rank | HOPF CONJECTURE | Riemannian foliations | deformations | positive transverse curvature | MANIFOLDS | Killing foliations
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2018, Volume 146, Issue 10, pp. 4389 - 4404
In this paper we introduce a C^r-perturbation procedure, with respect to the C^r-Epstein topology, for C^r-foliations by surfaces. Using this perturbation... 
MATHEMATICS | MATHEMATICS, APPLIED | SYSTEMS | FOLIATIONS
Journal Article
Journal fur die Reine und Angewandte Mathematik, ISSN 0075-4102, 12/2012, Volume 673, Issue 673, pp. 125 - 159
A manifold M with a foliation F is minimizable if there exists a Riemannian metric g on M such that every leaf of F is a minimal submanifold of (M, g). For a... 
MATHEMATICS | LIE FOLIATIONS | RIEMANNIAN FOLIATIONS
Journal Article
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9947, 04/2019, Volume 371, Issue 7, pp. 4895 - 4910
Classification results for complex Riemannian foliations are obtained. For open subsets of irreducible Hermitian symmetric spaces of compact type, where one... 
MATHEMATICS | Hermitian locally symmetric spaces | infinitesimal models | POLAR FOLIATIONS | SUBMANIFOLDS | Complex Riemannian foliations
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2015, Volume 2015, Issue 23, pp. 12840 - 12876
Here we state a conjecture concerning a local version of Brunella's alternative: any codimension one foliation in (C-3, 0) without germ of invariant surface... 
EXISTENCE | MATHEMATICS | REDUCTION | SINGULAR FOLIATIONS | HOLOMORPHIC FOLIATIONS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 09/2019, Volume 371, Issue 9, pp. 6289 - 6308
This article deals with the irreducible components of the space of codimension one foliations in a projective space defined by logarithmic forms of a certain... 
SPACE | MATHEMATICS | HOLOMORPHIC FOLIATIONS | IRREDUCIBLE COMPONENTS
Journal Article
Journal of Algebra, ISSN 0021-8693, 02/2016, Volume 447, pp. 397 - 423
Let M be an analytic manifold over R or C, θ a 1-dimensional Log-Canonical (resp. monomial) singular distribution and I a coherent ideal sheaf defined on M. We... 
Singular foliations | Resolution of singular varieties | Log-Canonical foliations | Monomial foliations | Analytic geometry | MATHEMATICS | BLOWING-UP | CHARACTERISTIC ZERO | FIELD | HIRONAKA RESOLUTION
Journal Article
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9947, 01/2019, Volume 371, Issue 2, pp. 949 - 969
We present a new list of irreducible components for the space of k-dimensional holomorphic foliations on P-n, n >= 3, k >= 2. They are associated to pull-back... 
MATHEMATICS | irreducible components | Holomorphic foliations | STABILITY
Journal Article
Journal of Symplectic Geometry, ISSN 1527-5256, 2017, Volume 15, Issue 3, pp. 719 - 739
A Poisson manifold (M-2n, pi) is b-symplectic if boolean AND(n) pi is transverse to the zero section. We prove an h-principle for open, b-symplectic manifolds,... 
MATHEMATICS | FOLIATIONS | DEFORMATIONS
Journal Article
by Xu, CY and Zhang, L
DUKE MATHEMATICAL JOURNAL, ISSN 0012-7094, 05/2019, Volume 168, Issue 7, pp. 1269 - 1301
We prove the nonvanishing theorem for 3-folds over an algebraically closed field k of characteristic p > 5. 
EXISTENCE | MATHEMATICS | FOLIATIONS | MODELS | SPACES | SHEAVES | SURFACES
Journal Article
JOURNAL OF DIFFERENTIAL GEOMETRY, ISSN 0022-040X, 07/2019, Volume 112, Issue 3, pp. 391 - 409
For a compact, orientable, irreducible 3-manifold with toroidal boundary that is not the product of a torus and an interval or a cable space, each boundary... 
SURGERY | TOPOLOGY | MATHEMATICS | MANIFOLDS | FOLIATIONS | KNOTS
Journal Article
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 10/2019, Volume 113, Issue 4, pp. 3921 - 3929
Non-dicritical codimension one foliations on projective spaces of dimension four or higher always have an invariant algebraic hypersurface. The proof relies on... 
Extension of subvarieties | Theoretical, Mathematical and Computational Physics | 37F75 | Mathematics, general | Mathematics | Algebraic separatrices | Applications of Mathematics | Foliations | 32D15 | EXISTENCE | MATHEMATICS | HOLOMORPHIC FOLIATIONS | SINGULAR FOLIATIONS | Hyperspaces | Algebra
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 06/2019, Volume 64, pp. 47 - 58
Given a geodesic line γ in the hyperbolic space Hn we formulate a necessary and sufficient condition for a function along this geodesic which measure the mean... 
Geodesic | Umbilical | Umbilical route | Foliation | Hypercycle | MATHEMATICS | MATHEMATICS, APPLIED | FOLIATIONS
Journal Article
2018, Series in applied and computational mathematics, ISBN 9789813230859, Volume 3, xi, 174 pages
Book
Journal of Differential Equations, ISSN 0022-0396, 12/2016, Volume 261, Issue 12, pp. 7157 - 7193
Related to the study of Hilbert's infinitesimal problem, is the problem of determining the existence and estimating the number of limit cycles of the linear... 
Reversible | Elliptic foliations | Lotka Volterra | Pencil of foliations | First integrals | Hamiltonian | Codimension four | MATHEMATICS | PERTURBATIONS
Journal Article
Journal für die reine und angewandte Mathematik, ISSN 0075-4102, 2014, Volume 694, Issue 694, pp. 49 - 84
In this paper, we study geometric properties of quotient spaces of proper Lie groupoids. First, we construct a natural stratification on such spaces using an... 
MATHEMATICS | LINEARIZATION | INTEGRABILITY | ALGEBROIDS | FOLIATIONS
Journal Article
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