arXiv research

In 2D, Finsler metrics with 3+ projective fields are projectively equivalent to Randers.

The paper constructs examples of compactifications for Einstein metrics.

Positive projectively flat metrics on Hopf manifolds are locally conformally flat-Kähler.

In the asymmetric setting, Hilbert's fourth problem asks to construct and study all (non-reversible) projective Finsler metrics: Finsler metrics defined on open, convex subsets of real projective $n$-space for which geodesics lie on projective lines. While asymmetric norms and Funk metrics provide many examples of esse…

The paper extends Ricci curvature in Finsler geometry and finds conditions for specific metrics.

Paper classifies Randers metrics based on Ricci curvature properties.

The paper studies projectively equivalent para-Kaehler metrics in 4D.

Study cylindrical symmetric Finsler metrics that are projectively flat.

The paper explores conditions for projective and dually flat metrics in Finsler spaces with Kropina changes of mth-root metrics.

Kähler-Einstein metrics on toric submanifolds cannot be induced by projective immersions.

Solves Lie's 3D metric problem for projective vector fields.

We study the following problem: given an Einstein metric on a manifold, characterize and study all Einstein metrics which are pointwise projective to the given one. By definition, two metrics are said to be pointwise projectively related if they have the same geodesics as point sets. This is closely related to Hilbert'…

Space of Zoll Finsler metrics on projective plane deformation retracts to round metric.

Paper introduces new Finsler metrics preserved under projective transformations.

Stenzel's metrics can't be projectively induced in complex projective space.

The paper characterizes complex Finsler metrics that are projectively flat or dually flat.

Study shows Ricci flat Calabi's metrics can't be projectively induced.

New Finsler metrics with constant flag curvature defined using Weyl-type curvature tensor.

A strictly convex real projective orbifold is equipped with a natural Finsler metric called the Hilbert metric. In the case that the projective structure is hyperbolic, the Hilbert metric and the hyperbolic metric coincide. We prove that the marked Hilbert length spectrum determines the projective structure only up to …

We correct a mistake in Shen Yibing, Yu Yaoyong, On Projectively Related Randers Metrics, International Journal of Mathematics 19}(2008), no. 5, 503--520, and prove the natural generalization of the projective Lichnerowicz-Obata conjecture for Randers metrics.

In this paper, we study a class of Finsler metrics composed by a Riemann metric $α=\sqrt{a_{ij}(x)y^i y^j}$ and a $1$-form $β=b_i(x)y^i$ called general ($α$, $β$)-metrics. We classify those projectively flat when $α$ is projectively flat. By solving the corresponding nonlinear PDEs, the metrics in this class are totall…

The paper defines conditions for projective changes between specific Finsler metrics.

We show that $PQ^ε$-projectivity of two Riemannian metrics introduced in \cite{Top2003} implies affine equivalence of the metrics unless $ε\in\{0,-1,-3,-5,-7,...\}$. Moreover, we show that for $ε=0$, $PQ^ε$-projectivity implies projective equivalence.

In this paper we introduce in study the projectively related complex Finsler metrics. We prove the complex versions of the Rapcsák's theorem and characterize the weakly Kähler and generalized Berwald projectively related complex Finsler metrics. The complex version of Hilbert's Fourth Problem is also pointed out. As an…

Study on null-projectability of Levi-Civita connections in neutral metrics.

Generalizes quantum integrability to all signatures for projectively equivalent metrics.

In Finsler geometry, there are infinitely many models of constant curvature. The Funk metrics, the Hilbert-Klein metrics and the Bryant metrics are projectively flat with non-zero constant curvature. A recent example constructed by the author is projectively flat with zero curvature. In this paper, we introduce a techn…

Study on Gauduchon manifolds finds metrics for projectively flat bundles.

New metric on geodesic currents connects different surface genera.

Finsler metrics of constant curvature characterized, with a Finslerian Beltrami Theorem.

Proves complex projective varieties are birational to cscK models.

New metrics defined in Finsler geometry with specific properties.

New examples found of complex manifolds with special metrics.

New Einstein metrics linked to projective structures and Toda equations.

The projective algebra p(M;F) (i.e the collection of all projective vector fields)of a Finsler space (M;F) is a finite-dimensional Lie algebra with respect to the usual Lie bracket. The projective algebra of Einstein metrics has been perpetually studied from physical and geometrical approaches. Here, the projective alg…

Two Kähler metrics on a complex manifold are called c-projectively equivalent if their $J$-planar curves coincide. These curves are defined by the property that the acceleration is complex proportional to the velocity. We give an explicit local description of all pairs of c-projectively equivalent Kähler metrics of arb…

Short note finds a new metric from sphere quotients.

Characterizes the largest two-systole in real projective spaces.

Trajectories of light rays in a static spacetime are described by unparametrised geodesics of the Riemannian optical metric associated with the Lorentzian spacetime metric. We investigate the uniqueness of this structure and demonstrate that two different observers, moving relative to one another, who both see the univ…

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

Solves classical problem with Kähler-Einstein metrics in complex projective spaces.

The paper proves an inequality for the second non-zero eigenvalue of the Laplacian on the projective plane.

The paper studies projectively and dually flat Finsler spaces with Randers changes.

Study of hyperbolic directions in convex projective geometry.

Study on projective and affine equivalence of sub-Riemannian metrics on manifolds.

In this paper, a characteristic condition of the projectively flat Kropina metric is given. By it, we prove that a Kropina metric $F=α^2/β$ with constant curvature $K$ and $\|β\|_α=1$ is projectively flat if and only if $F$ is locally Minkowskian.

Classifies Kähler-Einstein manifolds with specific properties.

We construct new explicit toric scalar-flat K{ä}hler ALE metrics on weighted projective spaces of non-compact type, which we use to obtain smooth extremal K{ä}hler metrics on appropriate resolutions of orbifolds. In particular, we obtain new extremal metrics certain resolutions of weighted projective spaces of compact …