arXiv research

Study cohomological and metric properties of non-Kähler complex manifolds.

We survey some basic geometric properties of the Funk metric of a convex set in $\mathbb{R}^n$. In particular, we study its geodesics, its topology, its metric balls, its convexity properties, its perpendicularity theory and its isometries. The Hilbert metric is a symmetrization of the Funk metric, and we show some pro…

Study Finsler metric measure manifolds' concentration properties.

New proof shows Cohen-Lyndon property for non-metric small-cancellation.

Study on properties of Oeljeklaus-Toma manifolds, including cohomology and metrics.

Analyzes properties of Hopf manifolds from analytic and metric perspectives.

Study shows how nonstandard hulls can contain metric completions.

As a generalization of the Schwarzschild solution, Vaidya presented a radiating metric to develop a model of the exterior of a star including its radiation field, called Vaidya metric. The present paper deals with the investigation on the curvature properties of Vaidya metric. It is shown that Vaidya metric can be cons…

The paper examines properties of spherical Finsler metrics, proving their semi-C-reducibility and conditions for vanishing mean stretch curvature.

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

We define metrics on Culler-Vogtmann space, which are an analogue of the Teichmuller metric and are constructed using stretching factors. In fact the metrics we study are related, one being a symmetrised version of the other. We investigate the basic properties of these metrics, showing the advantages and pathologies o…

New MMOTs define a generalized metric for multi-distribution transport.

This note establishes several integral identities relating certain metric properties of level hypersurfaces of Morse functions.

Introduces Finslerian convolution metrics and their properties.

Study properties of Kenmotsu manifolds with conformal η-Einstein soliton metrics.

Extends metric to Margulis spacetimes for convex properties.

We construct a family of Calabi-Yau metrics on $\C^3$ with properties analogous to the Taub-NUT metric on $\C^2$, and construct a family of Calabi-Yau 3-fold metric models on the positive and negative vertices of SYZ fibrations with properties analogous to the Ooguri-Vafa metric.

Study on Riemannian properties of SU_n using bi-invariant metric.

Study generalizations of chainability and compactness in metric spaces.

New structure with B-metric extends classical almost contact structures.

The paper solves navigation problems on conic Kropina manifolds and establishes curvature relationships.

Investigates special metrics in hypercomplex geometry.

A local deformation property for uniform embeddings in metric manifolds (LD) is formulated and its behaviour is studied in a formal view point. It is shown that any metric manifold with a geometric group action, typical metric spaces (Euclidean space, hyperbolic space and cylinders) and for κ\leq 0 the κ-cone ends over…

Study on fractional Sobolev metrics on curves, proving completeness and geodesic properties.

A spacetime denotes a pure radiation field if its energy momentum tensor represents a situation in which all the energy is transported in one direction with the speed of light. In 1989, Wils and later in 1997 Ludwig and Edgar studied the physical properties of pure radiation metrics, which are conformally related to a …

To evaluate disentangled representations several metrics have been proposed. However, theoretical guarantees for conventional metrics of disentanglement are missing. Moreover, conventional metrics do not have a consistent correlation with the outcomes of qualitative studies. In this paper we analyze metrics of disentan…

Study on curvature properties of N(κ)-contact metric manifolds with generalized Tanaka-Webster connection.

This paper provides details of the construction, properties and some applications of the ambient metric associated to a conformal class of metrics on a smooth manifold. Existence and uniqueness of formal expansions defining such metrics are considered. Equivalence with the expansions of associated Poincare metrics is e…

We study metric contraction properties for metric spaces associated with left-invariant sub-Riemannian metrics on Carnot groups. We show that ideal sub-Riemannian structures on Carnot groups satisfy such properties and give a lower bound of possible curvature exponents in terms of the datas.

The curvature properties of Robinson-Trautman metric have been investigated. It is shown that Robinson-Trautman metric admits several kinds of pseudosymmetric type structures such as Weyl pseudosymmetric, Ricci pseudosymmetric, pseudosymmetric Weyl conformal curvature tensor etc. Also it is shown that the difference $R…

The paper studies complex Finsler metrics and their equivalence to the Kobayashi metric.

Almost contact manifolds with B-metric are considered. Of special interest are the so-called vertical classes of the almost contact B-metric manifolds. Curvature properties of these manifolds are studied. An example of 5-dimensional manifolds is constructed and characterized.

The paper examines properties of self-affine Sierpiński sponges using metric invariants.

Let (M,g) be a Riemannian 4-manifold. The twistor space Z->M is a CP1-bundle whose total space Z admits a natural metric h. The aim of this article is to study properties of complex structures on (Z,h) which are compatible with the CP1-fibration and the metric h. The results obtained enable us to translate some metric …

H. A. Hayden [1] introduced the idea of semi-symmetric non-metric connection on a Riemannian manifold in (1932). Agashe and Chafle \cite{1} defined and studied semi-symmetric non-metric connection on a Riemannian manifold. In the present paper, we define a new type of semi-symmetric non-metric connexion in an almost co…

The paper proves geodesics and conic sections are length-minimizing under specific metrics.

We formalize the concept of a family of metric spaces satisfying a coarse property uniformly and we generalize finite decomposition complexity of Erik Guentner, Romain Tessera, and Guoliang Yu. Of particular interest are results determining sufficient conditions for a metric space to satisfy Property A of Guoliang Yu.

The aim of the present paper is to study the properties of Kenmotsu manifolds equipped with a non-symmetric non-metric connection. We also establish some curvature properties of Kenmotsu manifolds. It is proved that a Kenmotsu manifold endowed with a non-symmetric non-metric is irregular.

We show that if a group $G$ acts by isometries on a metric space $M$ which has asymptotic property C, such that the quasi-stabilizers of a point $x \in M$ have asymptotic dimension less than or equal to $n$, then $G$ itself has asymptotic property C.

Study properties of para-Kähler manifolds with conformal Einstein soliton metrics.

Investigates maps and properties in spaces with negative dimensions and curvature.

Clarifies metric properties on group power sets.

Study on properties of special Kähler metrics and their interplay.

The study of special metrics in various parabolic geometries.

Study geodesic properties of time series data using Wasserstein metric.

Study para-complex structures on specific Lie groups, finding explicit forms and properties.

The paper studies geodesic orbit properties in Finsler spaces.

This short note has been written as an Oberwolfach report for the workshop "Differentialgeometrie im Grossen". We discuss properties of metric spaces that at almost all points admit a tangent metric space. We explain why, under some mild assumptions, the tangents are almost surely subFinsler Carnot groups. We mention s…