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.
Develops a new algebraic framework for differential geometry of infinite dimensional spaces.
Study pseudo-hyperkähler geometry of curves in hyperkähler twistor spaces.
Since the end of the 19th century, and after the works of F. Klein and H. Poincaré, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen as a "limit" of both geometries. Then all the geometries that can be obtained in t…
Diffeology extends differential geometry to complex spaces.
New geometry based on Siegel upper half-space with volume formula.
Survey of recent metric geometry in Kähler metrics space.
Study of Teichmüller space geometry using infinitesimal and global methods.
Proposes a new phylogenetic tree space with biologically principled geometry.
Spinor representation in isotropic space via Laguerre geometry.
We survey some recent developments in the asymptotic geometry of the Hitchin moduli space, starting with an introduction to the Hitchin moduli space and hyperkähler geometry.
The target space geometry of abelian vector multiplets in theories in four and five space-time dimensions is called special geometry. It can be elegantly formulated in terms of Hessian geometry. In this review, we introduce Hessian geometry, focussing on aspects that are relevant for the special geometrie…
Characterizes higher rank model geometries using antipodal sets.
The paper examines curvature properties of twistor spaces.
The paper surveys pressure metrics in geometry and dynamics.
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive th…
We highlight the relation between the projective geometries of -dimensional Euclidean, spherical and hyperbolic spaces through the projective models of these spaces in the -dimensional Minkowski space, using a cross ratio notion which is proper to each of the three geometries.
In this paper, we first establish an equivalence theorem of Minkowski spaces by using results in centro-affine differential geometry. As an application in Finsler geometry, we gives some new characterizations of Berwald spaces.
New gauge condition fixes metric divergence in hyperbolic monopole spaces.
NLGS optimizes latent geometry for better model performance.
The paper examines the geometry of specific submanifolds in flag manifolds.
Study calibrated geometry in hyperkähler cones and their related spaces.
A timelike space is a Hausdorff topological space equipped with a partial order relation and a distance function satisfying a collection of axioms including a set of compatibility conditions between the partial order relation and the distance function. The distance function is defined only on a subset of the pr…
Study information geometry of warped product spaces, finding special connections.
We survey the geometry of Lagrange and Finsler spaces and discuss the issues related to the definition of curvature of nonholonomic manifolds enabled with nonlinear connection structure. It is proved that any commutative Riemannian geometry (in general, any Riemann--Cartan space) defined by a generic off--diagonal metr…
In this article, we summarize the results on symmetric conformal geometries. We review the results following from the general theory of symmetric parabolic geometries and prove several new results for symmetric conformal geometries. In particular, we show that each symmetric conformal geometry is either locally flat or…
Develops second order infinitesimal structures on Teichmüller space.
We present a list of open questions on various aspects of AdS geometry, that is, the geometry of Lorentz spaces of constant curvature -1. When possible we point out relations with homogeneous spaces and discrete subgroups of Lie groups, to Teichmüller theory, as well as analogs in hyperbolic geometry.
Theory developed for Hilbert geometry over valued fields, linking real and non-Archimedean geometries.
This thesis was motivated by a desire to understand the natural geometry of hyperbolic monopole moduli spaces. We take two approaches. Firstly we develop the twistor theory of singular hyperbolic monopoles and use it to study the geometry of their charge 1 moduli spaces. After this we introduce a new way to study the m…
The study identifies two sources of invariants in 2--nondegenerate CR geometries.
Some selected applications of KT and HKT geometries in string theory, supergravity, black hole moduli spaces and hermitian geometry are reviewed. It is shown that the moduli spaces of a large class of five-dimensional supersymmetric black holes are HKT spaces. In hermitian geometry, it is shown that a compact, conforma…
We obtain a topological interpretation for the space of harmonic forms for some complete Riemannian manifold : when the geometry at infinity is the geometry of a simply connected nilpotent Lie group, when the geometry at infinity is a symmetric space with non positive curvature and also when the geometry at infin…
We study the hypersymplectic geometry of the moduli space of solutions to Hitchin's harmonic map equations on a -bundle. This is the split-signature analogue of Hitchin's Higgs bundle moduli space. Due to the lack of definiteness, this moduli space is globally not well-behaved. However, we are able to construct a sm…
The lightlike geometry of codimension two spacelike submanifolds in Lorentz-Minkowski space has been developed in [Izumiya, S. and Romero Fuster, M. C. Selecta Mathematica (NS), 13 23--55 (2007)] which is a natural Lorentzian analogue of the classical Euclidean differential geometry of hypersurfaces. In this paper we i…
Study of harmonic Riemannian submersions from 3D geometries.
Uniform convexity in divisible domains leads to hyperbolic geometry.
PhD dissertation on Finsler geometry and gravity, focusing on Berwald spaces and exact solutions.
The paper explores geometry of probability measures and barycenter maps.
We construct natural Riemannian metrics on Seiberg-Witten moduli spaces and study their geometry.
In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of the intrinsic geometry is given. A new type of almost contact metric spaces, more precisely, Hermitian almost contact metric spac…
Quantizes geodesics in Kähler and Sasaki geometry.
Diffeologies unify infinite-dimensional geometry and PDEs, enhancing classical function spaces.
Introduces bounded scale measure and generalizes property A.
Characterizes Anosov flows via contact geometry.
Extends illumination bodies to non-Euclidean spaces and proves their volume derivative defines surface area.
Formula found for skinning map contraction in hyperbolic geometry.
The aim of the present paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism space (GAP-space). The Finsler structure is obtained from the vector fields forming the parallelization of the GAP-space. The resulting space, which we refer to as a Finslerized Pa…
After introducing the different boundary geometries of rank one symmetric spaces, we state and prove Fried's theorem in the general setting of all those geometries: a closed manifold with a similarity structure is either complete or the developing map is a covering onto the Heisenberg-type space deprived of a point.