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.
Novel approach to instantons on quaternionic Kähler manifolds.
The generalized Legendre transform method of Lindstrom and Rocek yields hyperkaehler metrics from holomorphic functions. Its main ingredients are sections of bundles over the twistor space satisfying a reality condition with respect to antipodal conjugation on the hyperkaehler sphere of complex structure…
The study examines sequences of 3D generalised monopoles with uniform bounds.
We construct propose an anzatz for Spin(7) metrics as an R-bundle over closed G2 structures. These G2 structures are R3 bundles over 4-dimensional compact quaternion Kahler spaces. The inspiration for the anzatz metric comes from the Bryant-Salamon construction of G2 holonomy metrics and from the fact that the twistor …
Under the action of the c-map, special Kahler manifolds are mapped into a class of quaternion-Kahler spaces. We explicitly construct the corresponding Swann bundle or hyperkahler cone, and determine the hyperkahler potential in terms of the prepotential of the special Kahler geometry.
We study a class of Hermitian metrics on complex manifolds, recently introduced by J. Fu, Z. Wang and D. Wu, which are a generalization of Gauduchon metrics. This class includes the one of Hermitian metrics for which the associated fundamental 2-form is -closed. Examples are given on nilmanifolds…
The paper characterizes curvature of quaternionic skew-Hermitian manifolds and constructs related geometric structures.
We consider a general 4n-dimensional quaternionic Kahler geometry with a free action of the torus T^(n+1). The toric action lifts onto the Swann bundle of the quaternionic Kahler space to a tri-holomorphic action that commutes with the standard H* action on the bundle. By matching Pedersen and Poon's generalized Gibbon…
We extend the twistor methods developed in our earlier work on linear deformations of hyperkahler manifolds [arXiv:0806.4620] to the case of quaternionic-Kahler manifolds. Via Swann's construction, deformations of a 4d-dimensional quaternionic-Kahler manifold are in one-to-one correspondence with deformations of it…
We give an overview of some recent results in hypersymplectic and para-quaternionic Kahler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic Kahler manifolds. These are used to classify examples with a fully homogeneo…
We classify both local and global Kähler structures admitting totally geodesic homothetic foliations with complex leaves. The main building blocks are related to Swann's twists and are obtained by applying Weinstein's method of constructing symplectic bundles to Kähler data. As a byproduct we obtain new classes of: hol…
The target space of a (4,0) supersymmetric two-dimensional sigma model with Wess-Zumino term has a connection with totally skew-symmetric torsion and holonomy contained in Sp(n)Sp(1) (resp. Sp(n)), QKT (resp. HKT)-spaces. We study the geometry of QKT, HKT manifold and their twistor spaces. We show that the Swann bundle…
Following the point of view of Gray and Hervella, we derive detailed conditions which characterize each one of the classes of almost quaternion-Hermitian -manifolds, . Previously, by completing a basic result of A. Swann, we give explicit descriptions of the tensors contained in the space of covariant derivati…
We prove Gray & Wolf's conjecture that a Riemannian homogeneous manifold admitting a strict nearly Kahler structure is 3-symmetric. We actually classify them in dimension 6 and use previous results of Swann, Cleyton and Nagy to prove the conjecture in higher dimensions.
New natural presentation of supergravity c-map using Hodge structures.
We study the rigid limit of a class of hypermultiplet moduli spaces appearing in Calabi-Yau compactifications of type IIB string theory, which is induced by a local limit of the Calabi-Yau. We show that the resulting hyperkahler manifold is obtained by performing a hyperkahler quotient of the Swann bundle over the modu…
Unified view of geometries with parallel skew torsion via submersions.
Flat Hermitian Lie algebras are always Kähler.
We define the operations of conformal change and elementary deformation in the setting of generalized complex geometry. Then we apply Swann's twist construction to generalized (almost) complex and Hermitian structures obtained by these operations and establish necessary and sufficient conditions for the Courant integra…
Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex co…
Study closed G2-structures with T3-symmetry, classifying them into types and deriving hypersymplectic structures.
The study of quotient structures in multi-graded bundles, including double vector bundles.
Study of semi-principal bundles using group actions and wreath products.
Establishes a framework for stringor bundles, proving their canonical isomorphism to Stolz-Teichner's.
In this study, we generalize double tangent bundles to double jet bundles. We present a secondary vector bundle structure on a 1-jet of a vector bundle. We show that 1-jet of a vector bundle carries two vector bundle structures, namely primary and secondary structures. We also show that the manifold charts induced by p…
This paper shows vector bundles and differential bundles are equivalent in smooth manifolds.
Introduces Darboux-Lie derivative for fiber bundles.
On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with an endomorphism twisted by the tangent bundle. The notion of generalized holomorphic bundle in Hitchin's generalized geometry coincides with that of co-Higgs bundle when the generalized complex manifold is ordinary complex. Schwarzenberger's r…
A stratified bundle is a fibered space in which strata are classical bundles and in which attachment of strata is controlled by a structure category of fibers. Well known results on fibre bundles are shown to be true for stratified bundles; namely the pull back theorem, the bundle theorem and the principal bundle theor…
We define double principal bundles (DPBs), for which the frame bundle of a double vector bundle, double Lie groups and double homogeneous spaces are basic examples. It is shown that a double vector bundle can be realized as the associated bundle of its frame bundle. Also dual structures, gauge transformations and conne…
Proves every equivariant vector bundle over toric manifolds is a Klyachko bundle.
Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical bundles. We study categorical principal bundles that are product bundles in the categor…
Symplectic fillings of prequantization bundles are shown to be disk bundles under certain conditions.
Identifies images of determinant morphism for specific co-Higgs bundles.
Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with strong bundling, it becomes hard to identify origins and destinations of individual…
The paper defines and explores vector bundles that can be turned and their properties.
Study projective flat vector bundles over Riemann surfaces using Wronskian line bundles.
The paper generalizes bundle gerbes over groupoids and their correspondence with PB groupoids.
Study geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
Generalizes Higgs bundles theory using a vector bundle twist.
Study of generalized vector bundles and their geometric tools.
The paper extends orthogonal decomposition results to hermitian Higgs bundles.
We present the notion of a filtered bundle as a generalisation of a graded bundle. In particular, we weaken the necessity of the transformation laws for local coordinates to exactly respect the weight of the coordinates by allowing more general polynomial transformation laws. The key examples of such bundles include af…
Introduces generalized principal bundles and connections, linking them to standard gauge theories.
Study proves existence of precotangent bundles for Grassmannians.
Investigates connections in Lie group bundles, focusing on geometric reduction.
Study of Pascal algebra matrices and their jet bundle map for vector bundles.
A bundle gerbe is constructed from an oriented smooth vector bundle of even rank with a fiberwise inner product, over a compact connected orientable smooth manifold with Riemannian metric. From a trivialization of the bundle gerbe is constructed an irreducible Clifford module bundle, a spinor bundle over the smooth fre…