arXiv research

Study cylindrical symmetric Finsler metrics with vanishing Douglas curvature.

This paper reviews Douglas curvature in Finsler geometry.

Study new warped metrics with vanishing Douglas curvature.

Douglas metrics are metrics with vanishing Douglas curvature which is an important projective invariant in Finsler geometry. To find more Douglas metrics, in this paper we consider a class of Finsler metrics called general $(α,β)$-metrics, which are defined by a Riemannian metric $α=\sqrt{a_{ij}(x)y^iy^j}$ and a $1$-fo…

In this paper, we study generalized Douglas-Weyl $(α, β)$-metrics. Suppose that an regular $(α, β)$-metric $F$ is not of Randers type. We prove that $F$ is a generalized Douglas-Weyl metric with vanishing S-curvature if and only if it is a Berwald metric. Moreover by ignoring the regularity, if $F$ is not a Berwald met…

The paper classifies specific types of metrics on 5D Lie groups.

Paper introduces new Finsler metrics preserved under projective transformations.

Study spherically symmetric Finsler metrics with specific curvature properties.

In this paper we study lifted left invariant $(α,β)$-metrics of Douglas type on tangent Lie groups. Let $G$ be a Lie group equipped with a left invariant $(α,β)$-metric of Douglas type $F$, induced by a left invariant Riemannian metric $g$. Using vertical and complete lifts, we construct the vertical and complete lifte…

In this paper the projective curvature invariants of a complex Finsler space are obtained. By means of these invariants the notion of complex Douglas space is then defined. A special approach is devoted to obtain the equivalence conditions that a complex Finsler space should be Douglas. It is shown that any weakly Kähl…

In this paper, we study a class of Finsler metrics called general $(α,β)$-metrics, which are defined by a Riemannian metric $α$ and a $1$-form $β$. We find an equation which is necessary and sufficient condition for such Finsler metric to be a Douglas metric. By solving this equation, we obtain all of general $(α,β)$-m…

In this paper, the Douglas curvature of (α,β)-metrics, a special class of Finsler metrics defined by a Riemannian metric αand a 1-form β, is studied. These metrics with vanishing Douglas curvature in dimension n\geq3 are classified by using a new class of metrical deformations called β-deformations. The result shows th…

In this paper, we consider the similarity and quasi-affinity problems for Hilbert modules in the Cowen-Douglas class associated with the complex geometric objects, the hermitian anti-holomorphic vector bundles and curvatures. Given a "simple" rank one Cowen-Douglas Hilbert module $\mathcal{M}$, we find necessary and su…

In this paper we classify all non-Berwaldian Randers metrics of Douglas type arising from invariant hyper-Hermitian metrics on simply connected four-dimensional real Lie groups. Also, the formulas of the flag curvature are given and it is shown that, in some directions, the flag curvature of the Randers metrics and the…

Defines a new Randers metric based on an existing one.

Square metrics $F=\frac{(α+β)^2}α$ are a special class of Finsler metrics. It is the rate kind of metric category to be of excellent geometrical properties. In this paper, we discuss the so-called singular square metrics $F=\frac{(bα+β)^2}α$. A characterization for such metrics to be of vanishing Douglas curvature is p…

New metrics defined in Finsler geometry with specific properties.

We give the explicit formulas of the flag curvatures of left invariant Matsumoto and Kropina metrics of Berwald type. We can see these formulas are different from previous results given recently. Using these formulas, we prove that at any point of an arbitrary connected non-commutative nilpotent Lie group, the flag cur…

In this paper, we investigate the spherically symmetric Finsler metrics with isotropic S-curvature and obtain a characterized equation. As an application, we prove that these metrics with Douglas type must be Randers metrics or Berwald metrics. This result leads to two classification theorems.

Study Cowen-Douglas operators from analytic function spaces.

The notion of a Douglas space of second kind of a Finsler space with $(α, β)$-metric was introduced by I. Y. Lee [9]. Since then, so many geometers have studied this topic e. g., [14]. In this paper, we prove that a Douglas space of second kind with special $$-metric $α+εβ+ k \frac{β^2}{α}$ is conformally trans…

In 2D, Finsler metrics are Douglas and generalized Berwald if they are Berwald or Randers.

New Finsler metrics constructed from $GDW$-metrics.

We show that two-dimensional conformally related Douglas metrics are Randers

In this paper, we study a class of Finsler metrics which contains the class of Berwald metrics as a special case. We prove that every Finsler metric in this class is a generalized Douglas-Weyl metric. Then we study isotropic flag curvature Finsler metrics in this class. Finally we show that on this class of Finsler met…

Develops noncommutative Cowen-Douglas theory for noncommuting operators.

In this paper, we construct a new class of Finsler manifolds called generalized isotropic Berwald manifolds which is an extension of the class of isotropic Berwald manifolds. We prove that every generalized isotropic Berwald manifold is a generalized Douglas-Weyl manifold. On a compact generalized isotropic Berwald man…

This paper describes the work of Jesse Douglas on the Plateau problem, work for which he was awarded a Fields Medal in 1936, and considers the contributions Tibor Rado made in the 1930s.

Paper bounds surface diameter and solves Plateau-Douglas problem.

The Funk-Finsler structure is constructed in hyperbolic models, including the Klein unit disc.

Solves Plateau-Douglas problem for singular configurations in general metric spaces.

Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.

In this paper, we consider doubly warped product (DWP) Finsler manifolds with some non-Riemannian curvature properties. First, we study Berwald and isotropic mean Berwald DWP-Finsler manifolds. Then we prove that every proper Douglas DWP-Finsler manifold is Riemannian. We show that a proper DWP-manifold is Landsbergian…

New algorithm solves maximal monotone inclusion problems.

Study shows bifurcation in optimal retirement planning.

The aim of the present paper is to provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism. Various known local results are generalized and other new intrinsic results are obtained. Nontrivial characterizations of projective changes are given. The fundamental proje…

The paper studies anisotropic conformal changes in pseudo-Finsler surfaces.

New algorithms solve nonconvex federated learning problems efficiently.

We adopt a vierbein formalism to study pseudo-Finsler spaces modeled on a pseudo-Minkowski space. We show that it is possible to obtain closed expressions for most of the geometric objects of the theory, including Berwald's curvature, Landsberg's tensor, Douglas' curvature, non-linear connection and Ricci scalar. These…

The Douglas Rachford algorithm is an algorithm that converges to a minimizer of a sum of two convex functions. The algorithm consists in fixed point iterations involving computations of the proximity operators of the two functions separately. The paper investigates a stochastic version of the algorithm where both funct…

New methods solve inverse problem for Lagrangians in calculus of variations.

The existence of Dirichlet minimizing multiple-valued functions for given boundary data has been known since pioneering work of F. Almgren. Here we prove a multiple-valued analogue of the classical Plateau problem of the existence of area-minimizing mappings of the disk. Specifically, we find, for $K \in \mathbb N,$ $k…

Optimal credit and consumption strategies in a switching market with default contagion.

Characterizes two-dimensional generalized Berwald metrics with vanishing S-curvature.

New Finsler metrics defined by Riemannian and 1-forms are studied.

In this lecture I review how a matrix/Azumaya-type noncommutative geometry arises for D-branes in string theory and how such a geometry serves as an origin of the master nature of D-branes; and then highlight an abundance conjecture on D0-brane resolutions of singularities that is extracted and purified from a work of …

Study Riemann-Finsler geometry on tangent bundles of Lie groups with 2D commutator subgroup.

We analyse the asymptotic behaviour of solutions of the Teichmüller harmonic map flow from cylinders, and more generally of `almost minimal cylinders', in situations where the maps satisfy a Plateau-boundary condition for which the three-point condition degenerates. We prove that such a degenerating boundary condition …