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.
Characterizes higher rank model geometries using antipodal sets.
We propose a definition of a "higher" version of the omni-Lie algebroid and study its isotropic and involutive subbundles. Our higher omni-Lie algebroid is to (multi)contact and related geometries what the higher generalized tangent bundle of Zambon and Bi/Sheng is to (multi)symplectic and related geometries.
The study characterizes geometries of hypersurfaces in warped product and conformal manifolds.
This article reviews -bundles and their applications in geometry and physics.
A novel method visualizes higher-dimensional spaces using hyperbolic geometry.
The paper reviews a correspondence between Double Field Theory and bundle gerbes.
New method finds open subsets with trivial holonomy for certain geometries.
Constructs geometries with nonvanishing curvature and essential automorphisms.
Higher Gauge Flow Models integrate higher geometry and symmetries into Generative Flow Models.
Introduces new connections in higher geometry.
This is a survey of motivations, constructions and applications of higher prequantum geometry. In section 1 we highlight the open problem of prequantizing local field theory in a local and gauge invariant way, and we survey how a solution to this problem exists in higher differential geometry. In section 2 we survey ex…
New concept of coarse medians for higher rank symmetric spaces.
Finsler geometry connects to higher-spin fields and curved-space Fronsdal equations.
We present an introduction to the geometry of higher order vector and co-vector bundles (including higher order generalizations of the Finsler geometry and Kaluza--Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by anholonomic frames with ass…
We study the spectral geometry of the Riemann curvature tensor for Pseudo-Riemannian manifolds and provide some examples illustrating the phenomena which can arise in the higher signature setting. Dedication: This paper is dedicated to the memory of our colleague Prof.G. Tsagas who studied the spectral geometry of Lapl…
Higher-order geometry modifies Newtonian dynamics and predicts anomalies in spacecraft motion.
The paper bounds higher Steklov eigenvalues of graphs on surfaces.
Enhances conformal geometry in higher dimensions with infinite-dimensional algebra.
Unified framework for observables in n-plectic geometry.
The paper studies higher geometric structures and connections on manifolds, constructing moduli stacks and proving equivalence criteria.
We develop a universal framework to study smooth higher orbifolds on the one hand and higher Deligne-Mumford stacks (as well as their derived and spectral variants) on the other, and use this framework to obtain a completely categorical description of which stacks arise as the functor of points of such objects. We choo…
The study sets limits on the complexity of Klein geometries.
We give an abstract formulation of the formal theory partial differential equations (PDEs) in synthetic differential geometry, one that would seamlessly generalize the traditional theory to a range of enhanced contexts, such as super-geometry, higher (stacky) differential geometry, or even a combination of both. A moti…
Unified field theory from higher-order Riemannian geometry.
Noncommutative geometry connects higher order connections to quantization.
We present an introduction to the geometry of higher order vector and co--vector bundles (including higher order generalizations of the Finsler geometry and Kaluza--Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by higher order nonlinear con…
Expands differential geometry to higher-order infinitesimals.
This paper describes several key discoveries in the 19th century that led to the modern theory of manifolds in the twentieth century: intrinsic differential geometry, projective geometry and higher dimensional manifolds and Riemannian geometry.
The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry.
Constructs Cartan geometries from automorphism behaviors.
Study pseudo-hyperkähler geometry of curves in hyperkähler twistor spaces.
In three dimensions, a `master theory' for all Thurston geometries requires imaginary flux. However, these geometries can be obtained from physical three-dimensional theories with various additional scalar fields, which can be interpreted as moduli in various compactifications of a higher-dimensional `master theory'. T…
This work explores symplectic structures on graded manifolds and higher Lie groupoids.
Kaluza-Klein Theory states that a metric on the total space of a principal bundle , if it is invariant under the principal action of , naturally reduces to a metric together with a gauge field on the base manifold . We propose a generalization of this Kaluza-Klein principle to higher principal bun…
We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)Kähler geometry.
The paper proves global invertibility for certain local diffeomorphisms and biholomorphisms in higher dimensions.
New model estimates higher-order interactions in stochastic processes using lower-dimensional projections.
Neural network learns from higher-order connections in molecules.
Using supervector fields and graded forms along a morphism, we study the geometry of ordinary differential superequations, extend the formalism of higher order Lagrangian mechanics to the graded context and prove a generalization of Noether's theorem.
Study derived Lie ∞-groupoids and algebroids in higher differential geometry.
We construct a parallel transport on higher loop spaces of a manifold in term of a higher dimensional generalization of iterated path integrals. Under mild assumptions, we define a de Rham complex on higher loop spaces and we recover a known result of Hain of a de Rham structure on higher homotopy groups of a manifold.…
Introduces Q-structures for mechanics using advanced geometry.
We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r,s) for certain values of (r,s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher or…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The generalization of some fundamental notions of the differential geometry and the t…
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…
We prove several Liouville-type non-existence theorems for higher order Codazzi tensors and classical Codazzi tensors on complete and compact Riemannian manifolds, in particular. These results will be obtained by using theorems of the connections between the geometry of a complete smooth manifold and the global behavio…
The monograph summarizes the author's results on the geometry of anholonomic and locally anisotropic interactions, published in J. Math. Phys., Nucl. Phys. B, Ann. Phys. (NY), JHEP, Rep. Math. Phys., Int. J. Theor. Phys. and in some former Soviet Union and Romanian scientific journals. The main subjects are in the theo…
For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry groups of simply connected Riemannian manifolds of pinched negative curvature. For sy…