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 paper explores quantum statistical manifolds and their autoparallelity, providing estimation-theoretical characterizations.
In this work a proposal for definition of twistors on generic curved spaces is exposed and investigated. We consider superpositions of nearly autoparallel and nearly geodesic maps (nearly conformal maps, nc-maps) of (pseudo-)Riemannian spaces as generalizations of conformal transforms. We introduce the nearly autoparal…
On the probability simplex, we can consider the standard information geometric structure with the e- and m-affine connections mutually dual with respect to the Fisher metric. The geometry naturally defines submanifolds simultaneously autoparallel for the both affine connections, which we call {\em doubly autoparallel s…
Researchers find conditions for autoparallels to be Finsler geodesics.
We formulate the theory of nearly autoparallel maps (generalizing conformal transforms) of locally anisotropic spaces and define the nearly autoparallel integration as the inverse operation to both covariant derivation and deformation of connections by nearly autoparallel maps. By using this geometric formalism we cons…
A second order variational description of the autoparallel curves of some differential-geometric connection for the third order Mathisson's 'new mechanics' of a relativistic free spinning particle is suggested starting from general requirements of invariance and 'variationality'.
The statistical analysis of data lying on a differentiable, locally Euclidean, manifold introduces a variety of challenges because the analogous measures to standard Euclidean statistics are local, that is only defined within a neighbourhood of each datapoint. This is because the curvature of the space means that the c…
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
We review the geometric setting of the field theory with locally anisotropic interactions. The concept of locally anisotropic space is introduced as a general one for various type of extensions of Lagrange and Finsler geometry and higher dimension (Kaluza--Klein type) spaces. The problem of definition of spinors on gen…
We construct a tangent bundle exponential map and locally autoparallel coordinates for geometries based on a general connection on the tangent bundle of a manifold. As concrete application we use these new coordinates for Finslerian geometries and obtain Finslerian geodesic coordinates. They generalise normal coordinat…
A special linear Lie group over the real number field and the quarternion field admits a projectivley flat affine connection. We show that parabolic subgroups are autoparallel submanifolds and give a criterion the induced connection is projectively equivalent to a flat affine connection.
Absolute parallelism geometry is frequently used for physical applications. It has two main defects, from the point of view of applications. The first is the identical vanishing of its curvature tensor. The second is that its autoparallel paths do not represent physical trajectories. The present work shows how these de…
Paper studies statistical manifolds with logarithmic divergences.
Develops a Kaluza-Klein theory in affine spaces without metric.
New formulation of Schrödinger connections preserves vector lengths in geometry.
The paper defines -normality for contact and paracontact manifolds and explores their properties.
We present a geometric approach to the field theory with higher order anisotropic interactions. The concepts of higher order space, or locally anisotropic, space (in brief, h-space, or la-space) are introduced as general ones for various types of higher order extensions of Lagrange and Finsler geometry and higher dimen…
Quantum connections replace metrics with operator inner products.
We develop a general theory for irreducible homogeneous spaces , in relation to the nullity of their curvature tensor. We construct natural invariant (different and increasing) distributions associated with the nullity, that give a deep insight of such spaces. In particular, there must exist an order-two tr…