Related papers: Projectively related complex Finsler metrics

A projective parameter of a geodesic on a Finsler space is defined to be solution of a certain ODE. Using projective parameter and Funk metric, one can construct a projectively invariant intrinsic pseudo-distance on a Finsler space. In the…

We give new characterizations of plurisubharmonic functions and Griffiths positivity of holomorphic vector bundles with singular Finsler metrics. As applications, we present a different method to prove plurisubharmonic variation of…

One of the most important problems in Finsler geometry is to classify Finsler metrics of scalar flag curvature. In this paper, we study the classification problem of Randers metrics of scalar flag curvature. Under the condition that $\beta$…

Complex Finsler vector bundles have been studied mainly by T. Aikou, who defined complex Finsler structures on holomorphic vector bundles. In this paper, we consider the more general case of a holomorphic Lie algebroid E and we introduce…

We establish a one-to-one correspondence between K\"ahler metrics in a given conformal class and parallel sections of a certain vector bundle with conformally invariant connection, where the parallel sections satisfy a set of non--linear…

In this short paper, we establish a closer relation between the Berwald scalar curvature and the $S$-curvature. In fact, we prove that a Finsler metric has isotropic Berwald scalar curvature if and only if it has weakly isotropic…

Given a semi-Riemannian $4$-manifold $(M,g)$ with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of K\"ahler metrics $g_K$ is constructed, defined on an…

We derive some necessary conditions on a Riemannian metric $(M, g)$ in four dimensions for it to be locally conformal to K\"ahler. If the conformal curvature is non anti--self--dual, the self--dual Weyl spinor must be of algebraic type $D$…

We obtain a partial parallelism of the complex structure on K\"ahler Finsler manifolds. As applications, we prove Synge-Tsukamoto theorem and Bonnet-Myers theorem for positively curved K\"ahler Finsler manifolds. Moreover, we generalize a…

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…

A finite projective plane, or more generally a finite linear space, has an associated incidence complex that gives rise to two natural algebras: the Stanley-Reisner ring $R/I_\Lambda$ and the inverse system algebra $R/I_\Delta$. We give a…

We introduce a new approach to Topological Data Analysis (TDA) based on Finsler metrics and we also generalize the classical concepts of Vietoris-Rips and Cech complexes within this framework. In particular, we propose a class of…

We search for Riemannian metrics whose Levi-Civita connection belongs to a given projective class. Following Sinjukov and Mikes, we show that such metrics correspond precisely to suitably positive solutions of a certain projectively…

Recently, the authors have proposed a new approach to the theory of random metrics, making an explicit link between probability measures on the space of metrics on a Kahler manifold and random matrix models. We consider simple examples of…

The authors have recently shown how direct limits of Hilbert spaces can be used to construct multi-resolution analyses and wavelets in $L^2(\R)$. Here they investigate similar constructions in the context of Hilbert modules over…

In this work we study the set of strictly accretive matrices, that is, the set of matrices with positive definite Hermitian part, and show that the set can be interpreted as a smooth manifold. Using the recently proposed symmetric polar…

We focus on the classical open problem of the classification of K\"ahler-Einstein manifolds that can be K\"ahler immersed into a complex projective space endowed with the Fubini-Study metric. In particular, we will deal with such problem in…

An extension of Riemmann's geometry into a direction dependent geometric structure is usually described by Finsler's geometry. Historically, this construction was motivated by the well-known Riemann's quartic length element example. Quite…

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 paper is related to the classification of special manifolds and projective special manifolds. One of the result of this paper is that, if the Weil-Petersson metric on a projective special manifold is complete, then the Hodge metrc and…