Related papers: Some Ricci-Flat $(\alpha,\beta)$-Metrics
For the two-parameter Mittag-Leffler function $E_{\alpha,\beta}$ with $\alpha > 0$ and $\beta \ge 0,$ we consider the question whether $|E_{\alpha,\beta}(z)|$ and $E_{\alpha,\beta}(\Re z)$ are comparable on the whole complex plane. We show…
We study almost Riemann solitons and almost Ricci solitons in an $(\alpha,\beta)$-contact metric manifold satisfying some Ricci symmetry conditions, treating the case when the potential vector field of the soliton is pointwise collinear…
A Finsler metric is geodesically reversible if geodesics remain geodesics after a change of orientation. Asymmetric norms on vector spaces and Funk metrics in the interior of convex bodies are examples of geodesically reversible metrics…
In this paper, we introduce a broad class of metrics on the slit tangent bundle of Finsler manifolds, termed \emph{$F$-natural metrics}. These metrics parallel the well-established $g$-natural metrics on the tangent bundles of Riemannian…
In this paper, we consider a Finsler space with a Randers change of Quartic metric F = $\sqrt[4]{\alpha^4 + \beta^4} + \beta$. The conditions for this space to be with reversible geodesics are obtained. Further, we study some geometrical…
The affine connection in a space-time with a maximally symmetric spatial subspace is derived using the properties of maximally symmetric tensors. The number of degrees of freedom in metric-affine gravity is thereby considerably reduced…
In this paper we consider strata of flat metrics coming from quadratic differentials (semi-translation structures) on surfaces of finite type. We provide a necessary and sufficient condition for a set of simple closed curves to be…
We study the cylindrical symmetric Finsler metrics. We obtain the system of differential equations of such metrics which are projectively flat. We give a family of solutions of this system. Examples are included.
Let $ G $ be a connected Lie group with real Lie algebra $ \mathfrak{g}$. Suppose $G$ is also a complex manifold. We obtain explicit holomorphic sectional and bisectional curvature formulas of left-invariant strongly pseudoconvex complex…
In this paper, we construct a set of new functionals of Ricci curvature on any Kaehler manifolds which are invariant under holomorphic transfermations in Kaehler Einstein manifolds and essentially decreasing under the Kaehler Ricci flow.…
The notion of a Douglas space of second kind of a Finsler space with $(\alpha, \beta)$-metric was introduced by I. Y. Lee [9]. Since then, so many geometers have studied this topic e. g., [14]. In this paper, we prove that a Douglas space…
A subset $A$ of a vector space $X$ is called $\alpha$-lineable whenever $A$ contains, except for the null vector, a subspace of dimension $\alpha$. If $X$ has a topology, then $A$ is $\alpha$-spaceable if such subspace can be chosen to be…
It is known that on a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive densities that is invariant under the action of the diffeomorphism group, is of the form $$…
The conformal properties of metrics are meaningful in Riemannian and Finsler geometry, and cubic metrics are useful in physics and biology. In this paper, we study the conformally flat cubic metrics with weakly isotropic scalar curvature.…
This paper is a continuation of our investigation of the anisotropic conformal change of a conic pseudo-Finsler surface $(M,F)$, namely, the change $\overline{F}(x,y)=e^{\phi(x,y)}F(x,y)$ \cite{first paper}. We obtain the relationship…
A graph is called Ricci-flat if its Ricci-curvatures vanish on all edges. Here we use the definition of Ricci-cruvature on graphs given in [Lin-Lu-Yau, Tohoku Math., 2011], which is a variation of [Ollivier, J. Funct. Math., 2009]. In this…
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…
The goal of this short paper is to give condition for the completeness of the Binet-Legendre metric in Finsler geometry. The case of the Funk and Hilbert metrics in a convex domain are discussed.
On a smooth closed Riemannian manifold, we show short time existence of smooth solutions to the $(\alpha,\beta)$-Ricci-Yamabe flow, which is a natural generalization of the Ricci flow and the Yamabe flow. We also establish some long time…
We construct a continuous 1-parameter family of smooth complete Ricci-flat metrics of cohomogeneity one on vector bundles over $\mathbb{CP}^2$, $\mathbb{HP}^2$ and $\mathbb{OP}^2$ with respective principal orbits $G/K$ the Wallach spaces…