13 citations · 19 across the 9 of their papers we have counts for
9 papers
On a generalization of Monge-Ampère equations and Monge-Ampère systems
Masahiro Kawamata, Kazuhiro Shibuya
We discuss Monge-Ampère equations from the view point of differential geometry. It is known that a Monge-Ampère equation corresponds to a special exterior differential system on a…
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…
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.
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…
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…
Rank two prolongations of second-order PDE and geometric singular solutions
Takahiro Noda, Kazuhiro Shibuya
In this present paper, we study geometric structures of rank two prolongations of implicit second-order partial differential equations (PDEs) for two independent and one dependent…
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.
Generalized Finsler structures on closed 3-manifolds
Sorin V. Sabau, Kazuhiro Shibuya, Gheorghe Pitis
An (I,J,K)-generalized Finsler structure on a 3-manifold is a generalization of a Finslerian structure, introduced in order to separate and clarify the local and global aspects in…
Moving frames on generalized Finsler structures
S. V. Sabau, K. Shibuya, H. Shimada
We study the relation between an R-Cartan structure α and an (I, J, K)- generalized Finsler structure on a 3-manifold showing the difficulty in finding a general transformation tha…