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arXiv research

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.

169,341 papers · 148 categories

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9 results for “Patterson-Walker”

Conformal Patterson-Walker metricsmath.DG

Generalizes classical construction to conformal structures.

problem Characterize and describe conformal structures from projective classes.

method Generalizes Patterson-Walker construction to split-signature conformal structures.

result Complete description of Einstein metrics and all symmetries.

conformal structures Patterson-Walker projective classes Einstein metrics symmetries

2016-04-28abs ↗pdf ↗

Fefferman-Graham ambient metrics of Patterson-Walker metricsmath.DG

New ambient metrics reveal properties of Walker metrics.

problem Characterizing Walker metrics using ambient metrics.

method Developed Fefferman-Graham ambient metrics for Walker metrics.

result Walker metrics have vanishing Q-curvature.

Fefferman-Graham ambient metrics Patterson-Walker metrics Q-curvature conformal structures

2016-08-24abs ↗pdf ↗

Symmetric Cartan calculus, the Patterson-Walker metric and Killing vector fieldsmath.DG

Develops symmetric Cartan calculus linking to Patterson-Walker metric.

problem No specific problem stated; focuses on developing a new calculus.

method Symmetric Cartan calculus, using torsion-free affine connections.

result Symmetric Cartan calculus is a complete analogue of classical Cartan calculus.

Cartan calculus symmetric derivative Patterson-Walker metric Killing vector fields

2025-01-21abs ↗pdf ↗

Induced almost para-Kähler Einstein metrics on cotangent bundlesmath.DG

The paper constructs almost para-Kähler-Einstein metrics on cotangent bundles.

problem Developing metrics on cotangent bundles associated with geometric structures.

method Using a construction involving geometric structures on a manifold

M

to associate an almost para-Kähler-Einstein metric on

T^*M

result Explicit formulae for these metrics are derived in specific geometric cases.

cotangent bundles almost para-Kähler-Einstein geometric structures Patterson-Walker metrics

2023-01-09abs ↗pdf ↗

A Projective-to-Conformal Fefferman-Type Constructionmath.DG

We study a Fefferman-type construction based on the inclusion of Lie groups ${\rm SL}(n+1)$ into ${\rm Spin}(n+1,n+1)$ . The construction associates a split-signature $(n,n)$ -conformal spin structure to a projective structure of dimension $n$ . We prove the existence of a canonical pure twistor spinor and a light-like co…

2015-10-12abs ↗pdf ↗

Symmetric Poisson geometry, totally geodesic foliations and Jacobi-Jordan algebrasmath.DG

Symmetric Poisson structures linked to geodesic foliations and Jordan algebras.

problem Understanding geometric structures related to geodesic foliations and dynamics.

method Introducing symmetric Poisson structures, proving correspondences with geodesic foliations and Jordan algebras.

result Symmetric Poisson structures correspond to totally geodesic foliations and Jacobi-Jordan algebras.

Symmetric Poisson geometry geodesic foliations Jacobi-Jordan algebras Patterson-Walker metric Newtonian equation

2025-08-21abs ↗pdf ↗

Generalized quasi-statistical structuresmath.DG

Study on quasi-statistical structures on manifolds and their properties.

problem Characterizing quasi-statistical structures and their integrability.

method Introducing generalized quasi-statistical structures and proving their integrability conditions.

result Any quasi-statistical structure on a manifold induces generalized quasi-statistical structures on its tangent and cotangent bundles.

quasi-statistical structures generalized tangent bundle affine connections Patterson-Walker metrics Sasaki metrics

2018-09-13abs ↗pdf ↗

Modified conformal extensionsmath.DG

Modified construction for conformal structures with twistor spinors.

problem Geometric construction and characterization of conformal structures.

method Geometric construction and characterization of

2n

-dimensional split-signature conformal structures.

result Explicit geometrically constructed Fefferman-Graham ambient metric with vanishing

Q

-curvature.

conformal structures twistor spinors Einstein metrics Fefferman-Graham ambient metric Q-curvature

2023-01-10abs ↗pdf ↗

Courant algebroid lifts and curved Courant algebroidsmath.DG

Introduces new construction for Courant algebroids and curved structures.

problem Understanding and classifying Courant algebroids and their lifts.

method Introduces Courant algebroid lift and curved Courant algebroids, establishing connections to various geometric structures.

result Established a classification of exact curved Courant algebroids and related connections to various geometric structures.

Courant algebroid curved Courant algebroid vector bundle connection Poisson geometry Lie algebras

2025-11-06abs ↗pdf ↗