Study estimates Bergman kernel on hyperbolic surfaces.
problem Estimating Bergman kernel on hyperbolic surfaces.
method Derive off-diagonal estimates for tensor-products of cotangent line bundles.
result Derived off-diagonal estimates for Bergman kernel.
Discrete vector bundles are important in Physics and recently found remarkable applications in Computer Graphics. This article approaches discrete bundles from the viewpoint of Discrete Differential Geometry, including a complete classification of discrete vector bundles over finite simplicial complexes. In particular,…
Lie groups of automorphisms of cotangent bundles of Lie groups are completely characterized and interesting results are obtained. We give prominence to the fact that the Lie groups of automorphisms of cotangent bundles of Lie groups are super symmetric Lie groups. In the cases of orthogonal Lie lgebras, semi-simple Lie…
In this paper we study some problems related to a vertical Liouville distribution (called vertical Liouville-Hamilton distribution) on the cotangent bundle of a Cartan space. We study the existence of some linear connections of Vrănceanu type on Cartan spaces related to some foliated structures. Also, we identify a cer…
Generalizes Tulczyjew triples for contact manifolds in Hamiltonian and Lagrangian formalisms.
problem Tackles the need for a geometric tool in contact manifolds.
method Introduces a generalized Tulczyjew triple for contact manifolds.
result Contact Hamiltonians and Lagrangians as sections of line bundles determine dynamics on contact phase space.
We study a problem of the geometric quantization for the quaternion projective space. First we explain a Kaehler structure on the punctured cotangent bundle of the quaternion projective space, whose Kaehler form coincides with the natural symplectic form on the cotangent bundle and show that the canonical line bundle o…
Constructs a geometric representation for holomorphic vector bundles.
problem Representing the second Beilinson-Chern class of holomorphic vector bundles.
method Constructs holomorphic bundle 2-gerbes to represent the second Beilinson-Chern class.
result Establishes precise relationship between holomorphic and smooth gerbes.
We give a method to construct Calabi-Yau metrics on G-invariant vector bundles over Kahler coset spaces G/H using supersymmetric nonlinear realizations with matter coupling. As a concrete example we discuss the CP^N model coupled with matter. The canonical line bundle is reproduced by the singlet matter and the cotange…
New symmetries and line bundles on hyperkähler spaces explored.
problem Exploring new symmetries on hyperkähler spaces.
method Introducing new continuous symmetries and their geometric implications.
result Found new types of symmetries and their associated line bundles.
Study geodesics on a modified cotangent bundle over Kählerian manifolds.
problem Investigate geodesics on a modified cotangent bundle.
method Introduced Berger-type deformed Sasaki metric, investigated Levi-Civita connections, and studied geodesics.
result Geodesic properties on modified cotangent bundles.
Stein and Weinstein structures are described for disk cotangent bundles of surfaces.
problem Characterizing Stein and Weinstein structures on disk cotangent bundles.
method Using Legendrian handlebody diagrams and symplectic/contact mappings.
result The canonical contact structure on the unit cotangent bundle of S is obtained via surgery.
Unique symplectic fillings found for specific cotangent bundles.
problem Symplectic fillings of unit cotangent bundles.
method Proved uniqueness up to diffeomorphism.
result Unique symplectically aspherical fillings found.
Describes a contact structure on a surface's cotangent bundle.
problem Contact structures on cotangent bundles of surfaces.
method Explicit open book decomposition.
result Explicit decomposition for canonical contact structure.
A genus one Lefschetz fibration is described for disk cotangent bundles of surfaces.
problem Describing Lefschetz fibrations on cotangent bundles.
method Explicit construction of genus one Lefschetz fibration.
result Explicit genus one open book decomposition for unit cotangent bundle.
Study fills nonorientable surfaces' cotangent bundles uniquely.
problem Minimal symplectic fillings of nonorientable surfaces.
method Cobordism and homeomorphism analysis.
result Unique minimal filling for Klein bottle.
The paper studies positivity properties of cotangent bundles in complex hyperbolic manifolds with cusps.
problem Positivity properties of cotangent bundles in complex hyperbolic manifolds with cusps.
method Analyzes intrinsic positivity properties of cotangent bundles using toroidal compactifications and ample line bundles.
result The cotangent bundle is ample modulo the boundary divisor for sufficiently small rational numbers.
Reduces cotangent bundles using symplectic methods.
problem Symplectic reduction of cotangent bundles.
method Locally conformally symplectic reduction at regular values.
result Proves theorem analogous to symplectic setting.
Study on Klein bottle's cotangent bundle using contact homology.
problem Understanding symplectic embeddings of toric domains into the Klein bottle's cotangent bundle.
method Combinatorial description of embedded contact homology, pseudoholomorphic curves.
result Obstruction theorem for symplectic embeddings and computation of Gromov width.
We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. We find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. We prove the characterization theorem…
Homotopy equivalence of cotangent bundles' function algebras is shown.
problem Understanding homotopy equivalence in cotangent bundles and their function algebras.
method Using shifted Poisson algebras and homotopy equivalence of bundles.
result Homotopy equivalent bundles have equivalent Poisson algebras.
Researchers create a new metric on complex projective space bundles.
problem Constructing a hyperkähler metric on complex projective space bundles.
method Explicit construction in local coordinates, using holomorphic isomorphism to coadjoint orbits.
result A hyperkähler metric on twisted cotangent bundles of CPn. Study natural foliations in cotangent bundles of Cartan spaces.
problem Characterize Cartan spaces with negative constant curvature.
method Analyze geometry of natural foliations in cotangent bundles.
result Obtained new characterizations of Cartan spaces with negative curvature.
Unique symplectic fillings of odd spheres' cotangent bundles proven.
problem Uniqueness of symplectic fillings for odd-dimensional spheres' cotangent bundles.
method Proof of uniqueness up to diffeomorphism.
result Unique symplectically aspherical fillings of odd spheres' cotangent bundles.
We construct a Kaehler structure on the punctured cotangent bundle of the Cayley projective plane whose Kaehler form coincides with the natural symplectic form on the cotangent bundle and we show that the geodesic flow action is holomorphic and is expressed in a quite explicit form. We also give an embedding of the pun…
The study realizes symmetric spaces as cotangent bundles and finds nonnegative curvature examples.
problem Understanding the geometry of symmetric spaces and their associated vector bundles.
method Realizing symmetric spaces as cotangent bundles of flag manifolds and constructing vector bundles.
result Examples of vector bundles over simply connected manifolds with nonnegative curvature but not nonnegative sectional curvature.
Study of Norden structures on cotangent bundles and their properties.
problem Exploring Norden structures on cotangent bundles and their properties.
method Using methods of generalized geometry, the study extends Norden structures from manifolds to their cotangent bundles.
result Cotangent bundles of complex Norden manifolds admit Norden structures, and under certain conditions, these structures are integrable or Kähler.
New method bounds intersections of exact Lagrangians in cotangent bundles.
problem Counting intersections of exact Lagrangian submanifolds in cotangent bundles.
method Sheaf quantization in Tamarkin's category for clean and degenerate intersections.
result Cardinality of intersections is bounded by sheaf Hom spaces.
We use minimal (or CMC) surfaces to describe 3-dimensional hyperbolic, anti-de Sitter, de Sitter or Minkowski manifolds. We consider whether these manifolds admit ``nice'' foliations and explicit metrics, and whether the space of these metrics has a simple description in terms of Teichmüller theory. In the hyperbolic s…
This article concerns cotangent-lifted Lie group actions; our goal is to find local and ``semi-global'' normal forms for these and associated structures. Our main result is a constructive cotangent bundle slice theorem that extends the Hamiltonian slice theorem of Marle, Guillemin and Sternberg. The result applies to a…
The paper studies symplectic geometry of cotangent bundles using sheaves theory.
problem Symplectic geometry of cotangent bundles.
method Application of sheaves theory of Kashiwara-Schapira to cotangent bundles.
result Recovery of several known theorems and proofs of new results.
Paper proves stability of flow in cotangent bundle for special Lagrangian submanifolds.
problem Stability of generalized Lagrangian mean curvature flow in cotangent bundle.
method New derivative estimates to weaken initial conditions and remove curvature constraints.
result Stability of flow near special Lagrangian submanifolds in cotangent bundle.
The paper proves conditions for minimal compact Kähler manifolds with vanishing second Chern class.
problem Conditions for minimal compact Kähler manifolds with vanishing second Chern class.
method Study of the abundance conjecture and associated Iitaka fibrations.
result For a minimal compact Kähler manifold, the second Chern class vanishes if and only if the cotangent bundle is nef and the canonical bundle has numerical dimension 0 or 1.
We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This generalizes the complete lift defined by I.Sato and the horizontal lift introduced by K.Yano and S.Ishihara. We study some geometric properties of this lift and its compatibility with symplectic …
The paper examines the smooth structure at singular points of diffeological spaces.
problem Understanding the smooth structure at singular points of diffeological spaces.
method Analyzes the derivatives along lines through the origin in the pencil diffeological space.
result The Zariski cotangent space at the origin is determined by derivatives along lines and forms a σ-continuous family. The paper classifies metrics on a Heisenberg group's cotangent bundle.
problem Classifying Riemannian metrics on a Heisenberg group's cotangent bundle.
method Left-invariant Riemannian metrics classification and uniqueness proof.
result Complex structure is unique and pseudoKähler metrics are Ricci flat.
The paper proves a theorem about special geometric structures.
problem Understanding properties of geometric structures under transformations.
method Proves a Chekanov-type theorem for spherized cotangent bundles.
result Properties of generating families persist under Legendrian isotopies.
We study the topology of exact and Stein fillings of the canonical contact structure on the unit cotangent bundle of a closed surface Σg, where g is at least 2. In particular, we prove a uniqueness theorem asserting that any Stein filling must be s-cobordant rel boundary to the disk cotangent bundle of Σg. For …
A new method simplifies contact Hamiltonian mechanics.
problem Traditional contact Hamiltonian mechanics is complex.
method Introduces sections of line bundles over contact manifolds.
result Reduces contact Hamiltonian formalism to symplectic.
Let G be compact Lie group. It is shown that the cotangent bundle of the complexification of G admits a hyperkahler structure which is invariant under left and right translations by elements of G. The proof is to realize the cotangent bundle of the complex group as a moduli space of solutions to Nahm's equations on the…
We obtain a locally symmetric Kaehler Einstein structure on the cotangent bundle of a Riemannian manifold of negative constant sectional curvature. Similar results are obtained on a tube around zero section in the cotangent bundle, in the case of a Riemannian manifold of positive constant sectional curvature. The obtai…
Extends geometric quantization to singular spaces.
problem Handling singular symplectic spaces in geometric quantization.
method Developed stratified pseudobundles to replace auxiliary information.
result Provided results for singular quotients of toric manifolds and cotangent bundles.
The article proves a long-term flow stability for zero sections of cotangent bundles of spheres.
problem Stability of Lagrangian mean curvature flows in cotangent bundles.
method Defined a generalized mean curvature vector field and showed the canonical connection on cotangent bundles is Einstein.
result Long-term existence and convergence of the zero section of cotangent bundles of spheres.
This encyclopedia article briefly reviews without proofs some of the main results in cotangent bundle reduction. The article recalls most the necessary prerequisites to understand the main results.
New exact Lagrangian tori found in torus cotangent bundle.
problem Existence of non-Hamiltonian isotopic Lagrangian tori.
method Constructing exact Lagrangian submanifolds in T∗Tn. result Found Lagrangian tori that are symplectically but not Hamiltonian isotopic to the zero section.
Paper defines Fisher co-metric on cotangent bundle and clarifies its relation to variance.
problem Defines Fisher co-metric on cotangent bundle and clarifies its relation to variance.
method Defines Fisher co-metric directly from Fisher metric without going through tangent bundle, using a natural correspondence between cotangent vectors and random variables.
result Clarifies the relation between Fisher co-metric and variance/covariance, trivializing the Cramér-Rao inequality.
Geometric study of thermodynamics using cotangent bundles.
problem Formulating classical thermodynamics using geometric structures.
method Contact geometry on cotangent bundles, homogeneous coordinates for intensive variables.
result Geometric formulation of thermodynamics with homogeneity properties.
Defines a distance function on a manifold using symplectic embeddings and recovers the metric.
problem Recovering a Riemannian metric from symplectic embeddings in cotangent bundles.
method Defines a distance-like function ρW using symplectic embeddings and recovers the metric when W is the unit disc-cotangent bundle. result The distance function ρW recovers the Riemannian metric when W is the unit disc-cotangent bundle. We extend the theorems concerning the equivariant symplectic reduction of the cotangent bundle to contact geometry. The role of the cotangent bundle is taken by the cosphere bundle. We use Albert's method for reduction at zero and Willett's method for non-zero reduction. We provide examples for both cases.