Related papers: Douglas metrics of (\alpha,\beta) type

Grauert showed that the existence of a complete K\"{a}hler metric does not characterize domains of holomorphy by constructing such metrics on the complements of complex analytic sets in a domain of holomorphy. In this note, we study the…

In this paper we consider the specification property for $(\alpha,\beta)$-shifts. When $\alpha=0$, Schmeling shows that the set of $\beta>1$ for which the $\beta$-shift has the specification property has the Lebesgue measure zero but has…

We consider the conformal class of the Riemannian product $g_0 + g$, where $g_0$ is the constant curvature metric on $S^m$ and $g$ is a metric of constant scalar curvature on some closed manifold. We show that the number of metrics of…

This article is a survey of results involving conformal deformation of Riemannian metrics and fully nonlinear equations.

In this paper, first we derive an explicit formula for the flag curvature of a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce it for naturally reductive homogeneous Finsler…

We use moving frame techniques to derive a notion of curvature for a class of piecewise-smooth Riemannian metrics called Regge metrics, showing that it is a measure that simultaneously satisfies the (weak) Cartan structure equations and the…

We present a primal only derivation of Mirror Descent as a "partial" discretization of gradient flow on a Riemannian manifold where the metric tensor is the Hessian of the Mirror Descent potential. We contrast this discretization to Natural…

We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some…

We consider fluctuations of error terms $\Delta(x)$ appearing in the asymptotic formula for a summatory function of coefficients of the Dirichlet series. These are quantified via $\Omega$ and $\Omega_{\pm}$ estimates. We obtain $\Omega$…

The paper contributes to the important and urgent problem to extend the physical theory of space-time in a Finsler-type way under the assumption that the isotropy of space is violated by a single geometrically distinguished spatial…

We consider a class of singular Riemannian manifolds, the deformed spheres $S^N_k$, defined as the classical spheres with a one parameter family $g[k]$ of singular Riemannian structures, that reduces for $k=1$ to the classical metric. After…

Grauert showed that it is possible to construct complete K\"{a}hler metrics on the complement of complex analytic sets in a domain of holomorphy. In this note, we study the holomorphic sectional curvatures of such metrics on the complement…

This work generalizes the results of an earlier paper by the second author, from Randers metrics to $(\alpha,\beta)$-metrics. Let $F$ be an $(\alpha,\beta)$-metric which is defined by a left invariant vector field and a left invariant…

In this paper, we study the weakly weighted Einstein-Finsler metrics. First, we show that weakly weighted Einstein-Kropina metrics must be of isotropic S-curvature with respect to the Busemann-Hausdorff volume form under a certain condition…

If $S$ is an infinite sequence over a finite alphabet $\Sigma$ and $\beta$ is a probability measure on $\Sigma$, then the {\it dimension} of $ S$ with respect to $\beta$, written $\dim^\beta(S)$, is a constructive version of Billingsley…

We consider geometries on the space of Riemannian metrics conformally equivalent to the widely studied Ebin L^2 metric. Among these we characterize a distinguished metric that can be regarded as a generalization of Calabi's metric on the…

Motivated by the fundamental theorem of calculus, and based on the works of Feller as well as Kac and Kre\u{\i}n, given an atomless Borel probability measure $\eta$ supported on a compact subset of $\mathbb{R}$, Freiberg and Z\"{a}hle…

The Gauss-Bonnet curvature of order $2k$ is a generalization to higher dimensions of the Gauss-Bonnet integrand in dimension $2k$, as the usual scalar curvature generalizes the two dimensional Gauss-Bonnet integrand. In this paper, we…

In this paper we study the behaviour of the holomorphic sectional curvature (or Gaussian curvature) of the Bergman metric of planar annuli. The results are then utilized to construct a domain for which the curvature is divergent at one of…

David Hilbert discovered in 1895 an important metric that is canonically associated to any convex domain $\Omega$ in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof assumes a certain degree of…