arXiv research

Study cylindrical symmetric Finsler metrics with vanishing Douglas curvature.

New Douglas metrics found in a specific Finsler class.

Study new warped metrics with vanishing Douglas curvature.

The paper classifies (α,β)-metrics with vanishing Douglas curvature.

Paper characterizes square metrics with vanishing Douglas curvature.

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, 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…

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…

New metrics defined in Finsler geometry with specific properties.

This paper reviews Douglas curvature in Finsler geometry.

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…

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

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

The paper studies special metrics on tangent Lie groups.

Paper introduces new Finsler metrics preserved under projective transformations.

The paper classifies special Randers metrics on Lie groups.

Study spherically symmetric Finsler metrics with specific curvature properties.

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…

Study on flag curvatures of specific metrics on Lie groups.

Defines a new Randers metric based on an existing one.

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 pseudo-Finsler spaces on pseudo-Minkowski space, deriving geometric objects.

Paper proves conformal transformation of special $(α, β)$-metrics to Douglas spaces.

Study Cowen-Douglas operators from analytic function spaces.

Two-dimensional metrics related by conformal transformations are also Randers.

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

New Finsler metrics constructed from $GDW$-metrics.

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.

Paper develops a constant step stochastic Douglas-Rachford algorithm for convex minimization.

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.

We extend the Boutet de Monvel Toeplitz index theorem to complex manifold with isolated singularities following the relative $K$-homology theory of Baum, Douglas, and Taylor for manifold with boundary. We apply this index theorem to study the Arveson-Douglas conjecture. Let $\ball^m$ be the unit ball in $\mathbb{C}^m$,…

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.

New adaptive stepsizes improve Douglas-Rachford and ADMM convergence.

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…

The paper studies curvature conditions on Kähler manifolds and proves comparison and vanishing theorems.

The paper studies Berwald scalar curvature properties in Finsler geometry.

New vanishing theorems for genera derived under almost nonnegative Ricci curvature.

Paper establishes a new formula for Atiyah-Patodi-Singer index using eta invariants.

The study classifies metrics with vanishing curvature on complex manifolds.

New algorithm solves maximal monotone inclusion problems.

Study shows bifurcation in optimal retirement planning.

We give a complete classification of homogeneous $(α,β)$-metrics with positive flag curvature and vanishing S-curvature.

Boundary bubbles form in almost minimal cylinders under specific conditions.

The study finds homogeneous geodesics in homogeneous Kropina spaces.