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On Asymmetric Distances

Andrea C.G. Mennucci (2013)

Analysis and Geometry in Metric Spaces

In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize the...

On Berwald and Wagner manifolds.

Vincze, Csaba (2008)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

On compatible linear connections of two-dimensional generalized Berwald manifolds: a classical approach

Csaba Vincze, Tahere Reza Khoshdani, Sareh Mehdi Zadeh Gilani, Márk Oláh (2019)

Communications in Mathematics

In the paper we characterize the two-dimensional generalized Berwald manifolds in terms of the classical setting of Finsler surfaces (Berwald frame, main scalar etc.). As an application we prove that if a Landsberg surface is a generalized Berwald manifold then it must be a Berwald manifold. Especially, we reproduce Wagner's original result in honor of the 75th anniversary of publishing his pioneering work about generalized Berwald manifolds.

On $ℝ$ -complex Finsler spaces.

Munteanu, Gheorghe, Purcaru, Monica (2009)

Balkan Journal of Geometry and its Applications (BJGA)

On Finsler connections.

Angel Montesinos (1979)

Revista Matemática Hispanoamericana

A new definition for lifts and lowerings is given, linking the different tensor algebras involved in the usual treatment of Finsler manifolds. By means of them, the relation between the different classes of linear connections is made clearer.

On Finslerian hypersurfaces given by $β$ -changes.

Kitayama, Masashi (2002)

Balkan Journal of Geometry and its Applications (BJGA)

On generalized Douglas-Weyl Randers metrics

Tayebeh Tabatabaeifar, Behzad Najafi, Mehdi Rafie-Rad (2021)

Czechoslovak Mathematical Journal

We characterize generalized Douglas-Weyl Randers metrics in terms of their Zermelo navigation data. Then, we study the Randers metrics induced by some important classes of almost contact metrics. Furthermore, we construct a family of generalized Douglas-Weyl Randers metrics which are not $R$ -quadratic. We show that the Randers metric induced by a Kenmotsu manifold is a Douglas metric which is not of isotropic $S$ -curvature. We show that the Randers metric induced by a Kenmotsu or Sasakian manifold is...

On higher order geometry on anchored vector bundles

Paul Popescu (2004)

Open Mathematics

Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle.

On isotropic Berwald metrics

Akbar Tayebi, Behzad Najafi (2012)

Annales Polonici Mathematici

We prove that every isotropic Berwald metric of scalar flag curvature is a Randers metric. We study the relation between an isotropic Berwald metric and a Randers metric which are pointwise projectively related. We show that on constant isotropic Berwald manifolds the notions of R-quadratic and stretch metrics are equivalent. Then we prove that every complete generalized Landsberg manifold with isotropic Berwald curvature reduces to a Berwald manifold. Finally, we study C-conformal changes of isotropic...

On $k$ -Hamilton geometry.

Kirkovits, Magdalen Sz. (1991)

Mathematica Pannonica

On nonlinear connections in higher order Lagrange spaces.

Roman, Marcel (2008)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

On projectable objects on fibred manifolds

Vasile Cruceanu, Marcela Popescu, Paul Popescu (2001)

Archivum Mathematicum

The aim of this paper is to study the projectable and $N$ -projectable objects (tensors, derivations and linear connections) on the total space $E$ of a fibred manifold $ξ$ , where $N$ is a normalization of $ξ$ .

On special hypersurface of a Finsler space with the metric $α + \frac{β^{n + 1}}{α^{n}}$ .

Narasimhamurthy, S.K., Aveesh, S.T., Nagaraja, H.G., Kumar, Pradeep (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

On the Chern-Weil homomorphism in Finsler spaces.

Kovács, Z. (2001)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

On the Finsler geometry of the Heisenberg group $H_{2 n + 1}$ and its extension

Mehri Nasehi (2021)

Archivum Mathematicum

We first classify left invariant Douglas $(α, β)$ -metrics on the Heisenberg group $H_{2 n + 1}$ of dimension $2 n + 1$ and its extension i.e., oscillator group. Then we explicitly give the flag curvature formulas and geodesic vectors for these spaces, when equipped with these metrics. We also explicitly obtain $S$ -curvature formulas of left invariant Randers metrics of Douglas type on these spaces and obtain a comparison on geometry of these spaces, when equipped with left invariant Douglas $(α, β)$ -metrics. More exactly, we show...

On the geometries of superior order.

Miron, Radu (1996)

Balkan Journal of Geometry and its Applications (BJGA)

On the geometry of some para-hypercomplex Lie groups

H. R. Salimi Moghaddam (2009)

Archivum Mathematicum

In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these spaces have constant negative scalar curvatures. Then by using left invariant Riemannian metrics introduced in the first part, we construct some left invariant Randers metrics of Berwald type. The explicit formulas for computing flag curvature have been obtained in...

On the homogeneous geometrical model of a Riemannian space.

Sandovici, Adrian (2003)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

On the projective Finsler metrizability and the integrability of Rapcsák equation

Tamás Milkovszki, Zoltán Muzsnay (2017)

Czechoslovak Mathematical Journal

A. Rapcsák obtained necessary and sufficient conditions for the projective Finsler metrizability in terms of a second order partial differential system. In this paper we investigate the integrability of the Rapcsák system and the extended Rapcsák system, by using the Spencer version of the Cartan-Kähler theorem. We also consider the extended Rapcsák system completed with the curvature condition. We prove that in the non-isotropic case there is a nontrivial Spencer cohomology group in the sequences...

On the Randers spaces of second order.

Roman, Marcel (2001)

Balkan Journal of Geometry and its Applications (BJGA)

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