arXiv research

Researchers describe a method to construct Ricci-flat metrics on a specific surface.

The paper proves properties of Kähler surfaces with zero scalar curvature.

The paper describes a new type of Kähler surfaces and their properties.

We present a classification of compact Kaehler manifolds admitting a hamiltonian 2-form (which were classified locally in part I of this work). This involves two components of independent interest. The first is the notion of a rigid hamiltonian torus action. This natural condition, for torus actions on a Kaehler manifo…

Study on existence of weighted extremal Kähler metrics on projective bundles.

Study of complex 3-folds with vanishing Bismut Ricci form via special Kähler geometry.

This thesis surveys various metrics on Riemann surface spaces.

Study on conditions for Randers metrics to be of constant Ricci curvature.

Proves existence and uniqueness of weighted metrics for smooth spaces.

New Finsler metrics constructed from $GDW$-metrics.

The paper introduces new Finsler metrics and associated weighted quasi-metrics.

We prove the equivalences of several classical complete metrics on the Teichmüller and the moduli spaces of Riemann surfaces. We use as bridge two new Kähler metrics, the Ricci metric and the perturbed Ricci metric and prove that the perturbed Ricci metric is a complete Kähler metric with bounded negative holomorphic s…

New metric defined for bounded symmetric domains.

Introduces Finslerian convolution metrics and their properties.

New balanced metrics introduced for SPD matrices, improving metric choice.

Survey of recent metric geometry in Kähler metrics space.

The paper defines metrics from Lie groups and conjectures they are Einstein metrics.

Study on geodesics of Finsler metrics derived from Riemannian metrics.

Paper examines conditions for singular square metrics to have constant curvature.

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 space of Kähler metrics to the space of Riemannian metrics, and we study its geome…

New Kähler metrics generalize Calabi's and relate to Fano manifolds.

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

We study the geodesic equation for the Dirichlet (gradient) metric in the space of Kaehler potentials. We first solve the initial value problem for the geodesic equation of the combination metric, including the gradient metric. We then discuss a comparison theorem between it and the Calabi metric. As geometric motivati…

The paper examines $(α,β)$-metrics and proves they are Berwald metrics under certain conditions.

Study on special Finsler metrics with conditions for Riemannian and isotropic properties.

Sharp estimates for Finsler metrics in convex domains.

The study examines Lee metrics on groups and their properties.

Survey of spectral, probabilistic, and deep metric learning methods.

Study shows convergence of Lagrangian submanifolds under certain metrics.

In this paper, we study an important class of Finsler metrics--square metrics. We give two expressions of such metrics in terms of a Riemannian metric and a 1-form. We show that Einstein square metrics can be classified up to the classification of Einstein Riemannian metrics.

Defines a new Randers metric based on an existing one.

The study characterizes Finsler metrics and proves their rigidity.

Investigates O(n)-invariant metrics on SPD matrices, extending kernel metrics.

Study Kähler-Einstein metrics on singular varieties, proving metric completion properties.

New interpretation of metrics on special geometric manifolds.

Proposes a method to select fair performance metrics through metric elicitation.

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 give two classes of positive semi-definite metrics on 2-manifolds. The one is called a class of Kossowski metrics and the other is called a class of Whitney metrics: The pull-back metrics of wave fronts which admit only cuspidal edges and swallowtails in $\boldsymbol{R}^3$ are Kossowski metrics, and t…

In this paper, we introduce the notion of Einstein-reversibility for Finsler met- rics. We study a class of p-power Finsler metrics determined by a Riemann metric and 1-form which are of Einstein-reversibility. It shows that such a class of Finsler metrics of Einstein-reversibility are always Einstein metrics. In parti…

metric-learn simplifies metric learning in Python.

Introduces new metric for Riemannian metrics, extending unbalanced optimal transport.

The paper explores learning metrics in low dimensions with bounds and complexities.

Study rough Riemannian metrics on manifolds, proving their connectedness and completeness.

Generalizes Thurston's asymmetric metric to flat metrics.

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 introduces two new metrics on outer space and shows fixed points for their actions.

Metric minimizing surfaces are locally CAT(0) in CAT(0) spaces.

This is the author's Ph.D. thesis, submitted to the University of Leipzig. It deals with the $L^2$ Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold. The main body of the thesis is a description of the completion manifold of metrics with respect to the $L^…