45 citations · 270 across the 37 of their papers we have counts for
27 papers · 1 filter
From dual connections to gravitational field equations -- the curvature and Einstein tensors of the - connection of a quasi-statistical manifold
Rattanasak Hama, Tiberiu Harko, Sorin V. Sabau
We present a detailed review of the mathematical foundations of the theory of the statistical and quasi-statistical manifolds, which recently have found many applications in genera…
Randers metrics on two-spheres of revolution with simple cut locus
Rattanasak Hama, Sorin V. Sabau
In the present paper, we study the Randers metric on two-spheres of revolution in order to obtain new families of Finsler of Randers type metrics with simple cut locus. We determin…
A Finsler metric of constant Gauss curvature on 2-sphere
I. Masca, S. V. Sabau, H. Shimada
We construct a concrete example of constant Gauss curvature on the 2-sphere having all geodesics closed and of same length.
Finslerian indicatrices as algebraic curves and surfaces
P. Chansri, P. Chansangiam, S. V. Sabau
We show how to construct new Finsler metrics, in two and three dimensions, whose indicatrices are pedal curves or pedal surfaces of some other curves or surfaces. These Finsler met…
Surfaces of revolution admitting strongly convex slope metrics
P. Chansagiam, P. Chansri, S. V. Sabau
This paper discusses the geometry of a surface endowed with a slope metric. We obtain necessary and sufficient conditions for any surface of revolution to admit a strongly convex s…
The geometry of a Randers rotational surface with an arbitrary direction wind
Rattanasak Hama, Sorin V. Sabau
In the present paper we study the global behaviour of geodesics on a Randers metric, defined on a topological cylinder, obtained as the solution of the Zermelo's navigation problem…
The geometry on the slope of a mountain
P. Chansri, P. Chansangiam, S. V. Sabau
The geometry on a slope of a mountain is the geometry of a Finsler metric, called here the {\it slope metric}. We study the existence of globally defined slope metrics on surfaces…
On the existence of convex functions on Finsler manifolds
Sorin V. Sabau, Pattrawut Chansangiam
We show that a non-compact (forward) complete Finsler manifold whose Holmes- Thompson volume is infinite admits no non-trivial convex functions. We apply this result to some Finsle…
The geometry of a positively curved Zoll surface of revolution
K. Kiyohara, S. V. Sabau, K. Shibuya
In this paper, we study the geometry of the manifolds of geodesics of a Zoll surface of positive Gauss curvature, show how these metrics induce Finsler metrics of constant flag cur…
The cut locus of a Randers rotational 2-sphere of revolution
Rattanasak Hama, Jaipong Kasemsuwan, Sorin V. Sabau
In the present paper we study the structure of the cut locus of a Randers rotational 2-sphere of revolution . We show that in the case when the Gaussian curvature of…
Berwald spaces of bounded curvature are Riemannian
Nathaphon Boonnam, Rattanasak Hama, Sorin V. Sabau
We prove that Berwald spaces whose flag curvature is nowhere vanishing are in fact Riemannian spaces. This means that any Berwald space with flag curvature bounded below by a posit…
Geodesics on strong Kropina manifolds
Sorin V. Sabau, Kazuhiro Shibuya, Ryozo Yoshikawa
We study the behavior of the geodesics of strong Kropina spaces. The global and local aspects of geodesics theory are discussed. Our theory is illustrated with several examples.
Kosambi-Cartan-Chern (KCC) theory for higher order dynamical systems
Tiberiu Harko, Praiboon Pantaragphong, Sorin V. Sabau
The Kosambi-Cartan-Chern (KCC) theory represents a powerful mathematical method for the investigation of the properties of dynamical systems. The KCC theory introduces a geometric…
A new perspective on the Kosambi-Cartan-Chern theory, and its applications
Tiberiu Harko, Praiboon Pantaragphong, Sorin Sabau
A powerful mathematical method for the investigation of the properties of dynamical systems is represented by the Kosambi-Cartan-Chern (KCC) theory. In this approach the time evolu…
The Co-Points of Rays are Cut Points of Upper Level Sets for Busemann Functions
Sorin V. Sabau
We show that the co-rays to a ray in a complete non-compact Finsler manifold contain geodesic segments to upper level sets of Busemann functions. Moreover, we characterise the co-p…
The geometry of a Randers rotational surface
Pakkinee Chitsakul, Rattanasak Hama, Sorin V. Sabau
We study the behavior of geodesics on a Randers surface of revolution. The main tool is the extension of Clairaut relation from Riemannian case to the Randers case. Moreover, we sh…
A variational problem for curves on Riemann-Finsler surfaces
Sorin V. Sabau, Kazuhiro Shibuya
We study the variational problem for -parallel curves on a Finslerian surface by means of Exterior Differential Systems using Griffiths' method. We obtain the conditions when th…
Topology of complete Finsler manifolds admitting convex functions
Sorin V. Sabau, Katsuhiro Shiohama
We study the topology of complete Finsler manifolds admitting convex functions
Riemannian and Finslerian spheres with fractal cut loci
Jinchi Itoh, Sorin V. Sabau
The present paper shows that for a given integer k greater than 2 it is possible to construct an at least k-differentiable Riemannian metric on the sphere of a certain dimension su…
A Gauss-Bonnet Type Formula on Riemann-Finsler surfaces with non-constant indicatrix volume
J. Itoh, S. V. Sabau, H. Shimada
We prove a Gauss-Bonnet type formula for Riemann-Finsler surfaces of non-constant indicatrix volume and with regular piecewise smooth boundary. We give a Hadamard type theorem for…
Some remarks on the geometry of Kropina spaces
Ryozo Yoshikawa, Sorin V. Sabau
Using the navigation data (h,W) of a Kropina space, we characterize weakly-Berwald Kropina spaces and Berwald Kropina spaces by means of the Killing vector field W and the parallel…
Metric structures associated to Finsler metrics
Sorin V. Sabau, Kazuhiro Shibuya, Hideo Shimada
We investigate the relation between weighted quasi-metric Spaces and Finsler Spaces. We show that the induced metric of a Randers space with reversible geodesics is a weighted quas…
Kropina metrics and Zermelo navigation on Riemannian manifolds
Ryozo Yoshikawa, Sorin V. Sabau
The present paper studies globally defined Kropina metrics as solutions of the Zermelo's navigation problem. Moreover, we characterize the Kropina metrics of constant flag curvatur…
On the existence of Generalized Unicorns on Surfaces
S. V. Sabau, K. Shibuya, H. Shimada
This paper addresses the problem of existence of generalized Landsberg structures on surfaces using the Cartan-Kähler Theorem and a Path Geometry approach.