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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.

168,657 papers · 148 categories

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← all fields·9 papers on “lie groups” in Differential Geometry · 1 month

On the structure of

2

-step nilpotent Lorentzian naturally reductive Lie groupsmath.DG

Study on special Lie groups with Lorentzian metrics.

problem Characterize structure of

2

-step nilpotent Lorentzian naturally reductive Lie groups.

method Develop framework for naturally reductive Lie groups, extend to Lorentzian context, analyze degenerate and non-degenerate cases.

result Complete structural description of naturally reductive

2

-step Lorentzian nilpotent Lie groups.

Lie groups Lorentzian metrics Naturally reductive Nilpotent Isotropic ideal

2026-07-20abs ↗pdf ↗

On non-positive Weyl connection on Lie groupsmath.DG

Paper finds non-positive Weyl connections on Lie groups, confirming a conjecture.

problem Finding non-positive invariant Weyl connections on Lie groups.

method Investigation of completely solvable Lie groups, focusing on SOL group.

result Only SOL admits non-positive Weyl connections, confirming a conjecture.

Weyl connections Lie groups non-positive completely solvable SOL group

2026-07-19abs ↗pdf ↗

The Bernstein-Gelfand-Gelfand (BGG) Construction: Algebra, Geometry, and Analysis; Part Imath.DG

Lecture notes on BGG complexes using Lie groups and algebras.

problem Constructing BGG complexes on open domains.

method Representation theory of semisimple Lie groups and Lie algebras.

result Introduction of BGG complexes with Lie group and algebra insights.

BGG complexes Lie groups Lie algebras representation theory differential forms

2026-07-12abs ↗pdf ↗

The curvature of left-invariant magnetic systemsmath.DG

Study magnetic curvature on Lie groups, extending Milnor's work.

problem Exploring magnetic curvatures on Lie groups.

method Computing magnetic curvatures and analyzing algebraic properties.

result Extending results from Milnor's classic paper on left-invariant metrics.

magnetic curvature Lie groups left-invariant metrics Heisenberg group

2026-07-10abs ↗pdf ↗

Torsion parallel pure spinors on neutral manifoldsmath.DG

Study of pure spinors on neutral manifolds with applications to supersymmetric solutions.

problem Characterizing pure spinors and their properties on neutral manifolds.

method Using the theory of real spinorial forms and differential systems, the square of pure spinors is analyzed.

result Non-pure spinors correspond to specific structures in signature (4,4), and parallel spinors are characterized by differential systems.

pure spinors neutral manifolds spinorial forms differential systems supersymmetric solutions

2026-07-07abs ↗pdf ↗

Quadratic Killing tensors on classical Lie groups are decomposablemath.DG

Quadratic Killing tensors on Lie groups are always decomposable.

problem Characterize Killing tensors on Lie groups.

method Analyzing the algebraic structure of Killing tensors on Lie groups.

result Quadratic Killing tensors on compact Lie groups are decomposable.

Killing tensor Lie groups decomposable quadratic geodesic flow

2026-07-05abs ↗pdf ↗

On a Theorem of Wang for Complex Homogeneous Manifoldsmath.DG

New Lie theoretic proof for complex homogeneous manifolds.

problem Proving compact homogeneous manifolds admit invariant complex structures.

method Lie theoretic proof using root space decomposition of compact Lie groups.

result New proof of Wang's theorem without advanced Lie algebra concepts.

Lie groups homogeneous manifolds complex structures Wang's theorem root space decomposition

2026-07-02abs ↗pdf ↗

Biholomorphism type of left-invariant complex structures on nilpotent Lie groupsmath.DG

Proves a complex structure conjecture for a specific type of Lie groups.

problem Proving a conjecture about left-invariant complex structures on nilpotent Lie groups.

method Analyzes simply connected, nilpotent Lie groups of dimension 2n.

result Proves biholomorphism to C^n for the specified Lie groups.

Lie groups complex structures biholomorphism nilpotent

2026-06-30abs ↗pdf ↗

Tanaka-Webster curvatures of surfaces in 3D Lie groups with a CR structuremath.DG

Study on surface geometry in Lie groups with CR structures.

problem Understanding surface curvature in Lie groups with CR structures.

method Defined Gauss and mean curvature in Tanaka-Webster geometry.

result Gave specific examples of surface curvature calculations.

Lie groups CR structures surface curvature Tanaka-Webster geometry

2026-06-28abs ↗pdf ↗