8 research outputs found
On Finsler surfaces with certain flag curvatures
In the present paper, we find out necessary and sufficient conditions for a
Finsler surface to be Landsbregian in terms of the Berwald curvature
-forms. We study Finsler surfaces which satisfy some flag curvature
conditions, viz., and
where is the Cartan scalar. In order to
do so, we investigate some geometric objects associated with the global Berwald
distribution of a
-dimensional Finsler metrizable nonflat spray . We obtain some
classifications of such surfaces and show that under what hypothesis these
surfaces turn to be Riemannian. The existence of a first integral for the
geodesic flow in each case has some remarkable consequences concerning rigidity
results. We prove that a Finsler surface with and
either or is Riemannian. Further, a Finsler surface
with and is Riemannian.Comment: 10 page
Gravity theory in SAP-geometry
The aim of the present paper is to construct a field theory in the context of
absolute parallelism (Teleparallel) geometry under the assumption that the
canonical connection is semi-symmetric. The field equations are formulated
using a suitable Lagrangian first proposed by Mikhail and Wanas. The
mathematical and physical consequences arising from the obtained field
equations are investigated.Comment: 14 pages, References added and a reference updated, minor correction
On Finslerized Absolute Parallelism spaces
The aim of the present paper is to construct and investigate a Finsler
structure within the framework of a Generalized Absolute Parallelism space
(GAP-space). The Finsler structure is obtained from the vector fields forming
the parallelization of the GAP-space. The resulting space, which we refer to as
a Finslerized Parallelizable space, combines within its geometric structure the
simplicity of GAP-geometry and the richness of Finsler geometry, hence is
potentially more suitable for applications and especially for describing
physical phenomena. A study of the geometry of the two structures and their
interrelation is carried out. Five connections are introduced and their torsion
and curvature tensors derived. Some special Finslerized Parallelizable spaces
are singled out. One of the main reasons to introduce this new space is that
both Absolute Parallelism and Finsler geometries have proved effective in the
formulation of physical theories, so it is worthy to try to build a more
general geometric structure that would share the benefits of both geometries.Comment: Some references added and others removed, PACS2010, Typos corrected,
Amendemrnts and revisions performe