arXiv research

Local rigidity results for Bergman and Kähler Carathéodory metrics on domains.

Study locally conformally balanced metrics on specific Lie algebras.

We study complex non-Kähler manifolds with Hermitian metrics being locally conformal to metrics with special cohomological properties. In particular, we provide examples where the existence of locally conformal holomorphic-tamed structures implies the existence of locally conformal Kähler metrics, too.

Investigate AR-Finsler metrics for local dual flatness and projective flatness.

Locally finite complexes with polyhedral $CAT(0)$ metrics are arborescent.

Three types of Einstein metrics are disqualified as potential local maxima.

Study local structure of Einstein metrics with boundary conditions.

Construct quaternionic-Kähler metrics from special Kähler manifolds with specific BPS structure variations.

Investigates locally symmetric polynomial metrics in Riemannian and Finslerian surfaces.

Study non-Kähler metrics on complex nilmanifolds, proving torus structure under certain conditions.

Constructs metrics with negative curvature on specific manifold types.

Classifies Kähler metrics with constant holomorphic curvature.

The requirement that a (non-Einstein) Kähler metric in any given complex dimension $m>2$ be almost-everywhere conformally Einstein turns out to be much more restrictive, even locally, than in the case of complex surfaces. The local biholomorphic-isometry types of such metrics depend, for each $m>2$, on three real param…

In this paper, we prove that every m-th root metric with isotropic mean Berwald curvature reduces to a weakly Berwald metric. Then we show that an m-th root metric with isotropic mean Landsberg curvature is a weakly Landsberg metric. We find necessary and sufficient condition under which conformal $β$-change of an m-th…

Locally adaptive nearest neighbors improve automated systems' performance and are easier to interpret.

Study connects two types of metrics on complex surfaces.

Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics, have a lot of applications in the real world. In this paper, we classify a class of singular $(α,β)$-metrics which are locally projectively flat with constant flag curvature in dimension $n= 2$ and $n \ge 3$ respectively. Further, we determine t…

We use maximal periodic flats to show that on a finite volume irreducible locally symmetric manifold of dimension $\geq 3$, no metric $g$ has more symmetry than the locally symmetric metric. We also show that if $g$ is a finite volume metric that is not locally symmetric, then its lift to the universal cover has discre…

Extends Lipschitz functions while preserving local constants.

New Einstein metrics found on complex manifolds.

We obtain an example of a compact locally conformal symplectic nilmanifold which admits no locally conformal Kähler metrics. This gives a new positive answer to a question raised by L. Ornea and M. Verbitsky.

Inspired by the role geometric structures play in our understanding of surfaces and three-manifolds, and Berger's observation that a surface of constant sectional curvature is determined up to local isometry by its Laplace spectrum, we explore the extent to which compact locally homogeneous three-manifolds are characte…

Study characterizes Einstein metrics in warped product spaces.

In this paper, we consider Kropina change of $m$-th root Finsler metrics. We find necessary and sufficient condition under which the Kropina change of an $m$-th root Finsler metric be locally dually flat. Then we prove that the Kropina change of an $m$-th root Finsler metric is locally projectively flat if and only if …

We classify those curvature-homogeneous Einstein four-manifolds, of all metric signatures, which have a complex-diagonalizable curvature operator. They all turn out to be locally homogeneous. More precisely, any such manifold must be either locally symmetric or locally isometric to a suitable Lie group with a left-inva…

Estimates Kähler metrics with noncollapsing volume under complex Monge-Ampère constraints.

Study evaluates local explanation methods for time series forecasting.

Totally geodesic subvarieties in moduli space are locally rigid.

Adapted metrics found on complex manifolds.

Two pseudo-Riemannian metrics $g$ and $\bar g$ are geodesically equivalent, if they share the same (unparameterized) geodesics. We give a complete local description of such metrics which solves the natural generalisation of Beltrami problem for pseudo-Riemannian metrics.

Study local properties of homogeneous ANR-spaces, proving dimension full-valuedness.

For all 0<t \leq 1, we define a locally Euclidean metric ρ_t on R^3. These metrics are invariant under Euclidean isometries and, if t increases to 1, converges to the Euclidean metric d_E. This research is motivated by expanding universe.

In this paper we give necessary and sufficient conditions for a connection in a plane bundle above a surface to be locally metric. These conditions are easy to be verified in any local chart. Also as a global result we give a necessary condition for two connections to be metric equivalent in terms of their Euler class.

Local Lorentzian theorem preserves metrics or makes them flat.

Local smoothing of metrics with small curvature, removing Ricci curvature condition.

This book offers to study locally compact groups from the point of view of appropriate metrics that can be defined on them, in other words to study "Infinite groups as geometric objects", as Gromov writes it in the title of a famous article. The theme has often been restricted to finitely generated groups, but it can f…

Study recovers Lorentzian metrics from boundary data, proving local rigidity.

We show that every Kato surface (or surface with a global spherical shell) admits a locally conformally Kaehler metric.

The object of the present paper is to study locally $φ$-symmetric LP-Sasakian manifolds admitting semi-symmetric metric connection and obtain a necessary and sufficient condition for a locally $φ$-symmetric LP-Sasakian manifold with respect to semi-symmetric metric connection to be locally $φ$-symmetric LP-Sasakian man…

Locally symmetric metrics on 4-manifolds with non-negative curvature.

Classifies Einstein metrics on 4-manifolds with specific symmetry groups.

We review the properties of the Morse-Novikov cohomology and compute it for all known compact complex surfaces with locally conformally Kähler metrics. We present explicit computations for the Inoue surfaces $\mathcal{S}^0$, $\mathcal{S}^+$, $\mathcal{S}^-$ and classify the locally conformally Kähler (and the tamed loc…

A necessary condition for a connection in a vector bundle to be locally metric is for its curvature matrix, which consists of $2$ forms, to be skew symmetric with respect to some local frame. In this paper we give a simple algorithm that can be used to decide when a matrix of $2$ forms is equivalent to a skew symmetric…

The paper studies LCAK metrics on complex manifolds and their properties.

We investigate isometric immersions of locally conformally Kaehler metrics into Hopf manifolds. In particular, we study Hopf-induced metrics on compact complex surfaces.

Study shows zero Pontrjagin classes for sprays.

The local structure of Finsler metrics of constant flag curvature have been historically mysterious. It is proved that every Matsumoto metric of constant flag curvature on a manifold of dimension n \geq 3 is either Riemannian or locally Minkowskian.

Three distinct 3D components found in local extremal Kähler metrics.