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.
The study explores properties of metric connections with skew torsion and their curvature identities.
problem Investigating curvature properties of metric connections with skew torsion.
method Analyzing the curvature and torsion properties of metric connections with skew torsion.
result Necessary and sufficient conditions for a metric connection with skew torsion to satisfy the Riemannian first and second Bianchi identities are presented.
Derivative estimates for pluriclosed flow control curvature and torsion.
problem Deriving derivative estimates for the pluriclosed flow.
method Control higher order derivatives of Chern curvature and torsion using Chern curvature; derive an estimate for torsion tensor using Chern Ricci curvature in dimension two; find a monotonic quantity in Hermitian-symplectic case.
result All Hermitian-symplectic solitons are Kähler Ricci solitons.
A geometric interpretation of curvature and torsion of linear transports along paths is presented. A number of (Bianchi type) identities satisfied by these quantities are derived. The obtained results contain as special cases the corresponding classical ones concerning curvature and torsion of linear connections.
A natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric is constructed. The class of these manifolds, where the considered connection exists, is determined. Some curvature properties for this connection, when the corresponding curvature tensor has the properties of the curvatu…
problem Investigate instanton properties in G2 and Spin(7) manifolds.
method Analyze the characteristic and torsion connections on G2 and Spin(7) manifolds, focusing on parallel torsion and Lee forms.
result Conditions for the curvature of the characteristic connection to be a G2 instanton and for the torsion connection to be a Spin(7) instanton are established.
Establishes necessary conditions for cylindrical curves using curvature and torsion.
problem Geometrically identifying curves on cylindrical surfaces.
method Identifying a fundamental function ψ and reducing the problem to a compatibility condition between an eighth-degree polynomial and a differential equation for ψ.
result Proves that for curves with constant curvature κ0 = 1/ρ, the torsion τ admits an explicit, exact solution.
Curvature and torsion of linear transports along paths in, respectively, vector bundles and the tangent bundle to a differentiable manifold are defined and certain their properties are derived.
We describe the curves of constant (geodesic) curvature and torsion in the three-dimensional round sphere. These curves are the trajectory of a point whose motion is the superposition of two circular motions in orthogonal planes. The global behavior may be periodic or the curve may be dense in a Clifford torus embedded…
Torsions, curvatures, structure equations and Bianchi identities for locally anisotropic superspaces (containing as particular cases different supersymmetric extensions and prolongations of Riemann, Finsler, Lagrange and Kaluza--Klein spaces) are investigated.
This paper is devoted to the first systematic investigation of manifolds that are Einstein for a connection with skew symmetric torsion. We derive the Einstein equation from a variational principle and prove that, for parallel torsion, any Einstein manifold with skew torsion has constant scalar curvature; and if it is …
This paper finds a metric on \(S^2 imes T^2\) with strictly positive biorthogonal curvature using an affine connection with antisymmetric torsion.
problem Existence of a Riemannian metric on \(S^2 imes T^2\) with strictly positive biorthogonal curvature.
method Introducing an affine connection with antisymmetric torsion calibrated via non-trivial cohomology classes, which allows overcoming topological constraints.
result Demonstrates the construction of a metric on \(S^2 imes T^2\) with strictly positive biorthogonal curvature.