A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Proves conjecture about foliations on curved spaces.
Classifies polar foliations on symmetric spaces.
The leaf space of a Killing Riemannian foliation is a diffeological quasifold.
Classifies foliations on specific symmetric spaces.
The paper studies foliations on homogeneous spaces and identifies specific foliations.
Positive curvature forces foliation leaf spaces to have boundaries.
Study of foliations on symmetric spaces and mean curvature flow results.
Classifies foliations of complex and quaternionic projective spaces.
Study natural foliations in cotangent bundles of Cartan spaces.
Develops twistor theory for foliated manifolds, proving orbifold results.
Classifies actions on complex space forms with Lagrangian orbits.
The space of broken hyperbolic structures generalizes the Teichmüller space of a punctured surface, and the space of projectivized broken measured foliations (equivalently, the space of projectivized affine foliations) generalizes the space of projectivized measured foliations. Just as projectivized measured foliations…
Study local foliations of surfaces with constant mean curvature and constant expansion in space-time.
Let (M,F) be a foliated manifold. We study the relationship between the basic cohomology Hb(M,F) of the foliation and the De Rham cohomology H(DF) of the space of leaves M/F as a quotient diffeological space. We prove that for an arbitrary foliation there is a morphism from H(DF) to Hb(M,F). It is an isomorphism when F…
In this paper, we study stability for harmonic foliations on locally conformal Kähler manifolds with complex leaves. We also discuss instability for harmonic foliations on compact submanifolds immersed in Euclidean spaces and compact homogeneous spaces.
Irreducible isoparametric foliations of arbitrary codimension q on complex projective spaces CP^n are classified, except if n=15 and q=1. Remarkably, there are noncongruent examples that pull back under the Hopf map to congruent foliations on the sphere. Moreover, there exist many inhomogeneous isoparametric foliations…
Theorems prove upper bounds for foliations on closed Alexandrov spaces.
Equivalences between conformal foliations on Euclidean -space, Hermitian structures on Euclidean -space, shear-free ray congruences on Minkowski -space, and holomorphic foliations on complex -space are explained geometrically and twistorially; these are used to show that 1) any real-analytic complex-valued …
The topology of the Hausdorff leaf spaces (HLS) for a codim-1 foliation is the main topic of this paper. At the beginning, the connection between the Hausdorff leaf space and a warped foliations is examined. Next, the author describes the HLS for all basic constructions of foliations such as transversal and tangential …
This thesis is concerned with equidistant foliations of Euclidean space, i.e. partitions into complete, connected, properly embedded smooth submanifolds. The space of leaves is an Alexandrov space of nonnegative curvature and the canonical projection is a submetry. Generalizing a result of Gromoll and Walschap we show …
Lie foliations with symmetric leaves are smoothly conjugate to homogeneous ones.
Investigates singular Finsler foliations on -spaces and their relation to Riemannian foliations.
We prove that a polar foliation of codimension at least three in an irreducible compact symmetric space is hyperpolar, unless the symmetric space has rank one. For reducible symmetric spaces of compact type, we derive decomposition results for polar foliations.
The study proves a transverse diameter theorem for Lorentzian foliations.
Survey and extend work on singular foliations in diffeology.
Sphere theorems extended to Riemannian foliations with new results on curvature and leaf spaces.
Paper extends foliation results in higher dimensions for Schwarzschild spaces.
A foliation on a Riemannian manifold is hyperpolar if it admits a flat section, that is, a connected closed flat submanifold that intersects each leaf of the foliation orthogonally. In this article we classify the hyperpolar homogeneous foliations on every Riemannian symmetric space of noncompact type.
New foliations constructed from contact pairs, revealing flexible taut foliations.
Classification extended for reducible symmetric spaces.
Some properties of Riemannian foliations on closed manifolds are generalized to compact equicontinuous foliated spaces. For instance, it is proved that all holonomy covers of the leaves are quasi-isometric to each other.
Study shows conditions for continuity of foliated homeomorphisms action on space of leaves.
We prove that the Teichmüller space of the Hirsch foliation (a minimal foliation of a closed 3-manifold by non-compact hyperbolic surfaces) is homeomorphic to the space of closed curves in the plane. This allows us to show that that the space of hyperbolic metrics on the foliation is a trivial principal fiber bundle. A…
The topological Molino's description of equicontinuous foliated spaces, studied by the first author and Moreira Galicia, gives conditions to reduce their study to the particular case where the holonomy pseudogroup can be represented by a pseudogroup on some local group generated by some of its local left translatio…
We prove that, up to isometric congruence, there are exactly 2n+1 homogeneous polar foliations of the complex hyperbolic space. We also give an explicit description of each of these foliations.
Integral formulae for foliated Riemannian manifolds provide obstructions for existence of foliations or compact leaves of them with given geometric properties. Recently, we associated a new Riemannian metric to a codimension-one foliated Finsler space and proved integral formulae for general and for Randers spaces. In …
We give a survey of the approaches to classifying foliations, starting with the Haefliger classifying spaces and the various results and examples about the secondary classes of foliations. Various dynamical properties of foliations are introduced and discussed, including expansion rate, local entropy, and orbit growth …
Research proves the connectedness of classifying spaces for Haefliger structures.
Study the structure of Kähler foliations with negative Ricci curvature.
Investigates Künneth formula for foliated de Rham cohomology, overcoming non-Hausdorff issues.
Survey on collapsing manifolds using group actions and foliations.
New findings on -spaces and taut foliations in hyperbolic links.
The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional structure which generalizes the notion of atlas. The approach is compared with the known ones that use the Grothendieck topos…
Extends Masur's divergence theorem to complex tori and Kummer surfaces.
Study properties of semi-symmetric Lorentzian spaces, foliated manifolds.
Consider a singular Riemannian foliation (s.r.f for short) on a compact manifold. By successive blow-ups along the strata, we construct a regular Riemannian foliation on another compact Riemannian manifold and a desingularization map that projects leaves of the regular Riemannian foliation into leaves of the s.r.f. Thi…
New foliations found in 3D spaces from positive braids.
The paper studies constant harmonic mean curvature surfaces in Schwarzschild spaces, proving they foliate the space.