Journal of Finsler Geometry and its Applications
https://jfga.uma.ac.ir/
Journal of Finsler Geometry and its Applicationsendaily1Thu, 01 Dec 2022 00:00:00 +0330Thu, 01 Dec 2022 00:00:00 +0330Some volume comparison theorems on Finsler manifolds of weighted Ricci curvature bounded below
https://jfga.uma.ac.ir/article_1928.html
This paper mainly studies the volume comparison in Finsler geometry under the condition that the weighted Ricci curvature Ric&infin;&nbsp;has a lower bound. By using the Laplacian comparison theorems of distance function, we characterize the growth ratio of the volume coefficients. Further, some volume comparison theorems of Bishop-Gromov type are obtained.One pde arising from concircular transformation on Finsler spaces.
https://jfga.uma.ac.ir/article_2240.html
In this paper, We characterize a Finsler manifold admitting a conformal transformation such that the difference of the two Ricci tensors is a constant multiple of the metric. Furthermore, we find some results on Finsler manifolds with constant flag curvature admiting a special conformal transformation.Shen's L-Process on the Chern Connection
https://jfga.uma.ac.ir/article_2241.html
&lrm;The notion of Shen's process was introduced by Tayebi-Najafi in order to construct the Shen connection from the Berwald connection&lrm;. &lrm;In this paper&lrm;, &lrm;we study the connection obtained by Shen's L-process on the Chern connection&lrm;. &lrm;Let (M&lrm;, &lrm;F) be a Finsler manifold&lrm;. &lrm;Suppose that D is the linear torsion-free connection obtained by Shen's L-process on Chern's connection&lrm;. &lrm;First&lrm;, &lrm;we show the existence and uniqueness of D&lrm;. &lrm;Then&lrm;, &lrm;we prove that their hv-curvature coincides if and only if F is a Riemannian &lrm;metricSome results in generalized symmetric square-root spaces
https://jfga.uma.ac.ir/article_1929.html
In this paper, we study generalized symmetric Finsler spaces with special (&alpha; , &beta; ) -space. In fact, we study this spaces with square-root metric and we prove that generalized symmetric (&alpha; , &beta; ) -spaces with square-root metric must be Riemannian.On 3-Dimensional Finsler Manifolds
https://jfga.uma.ac.ir/article_1930.html
Every Landsberg metric and every Landsbeg metric is a weakly Landsberg metric, but the converse is not true generally. Let (M, F) be a 3-dimensional Finsler manifold. In this paper, we find a condition under which the notions of weakly Landsberg metric and Landsberg metric are equivalent.Angle geometry between Teichmüller geodesic segments
https://jfga.uma.ac.ir/article_2242.html
In this paper we discuss some results related to angle between geodesic segments in an infinite dimensional and an asymptotic Teichm&uuml;ller space. Also, we construct a geodesic triangle in Universal Teichm&uuml;ller space and calculate all of its interior angles.On Conformally Flat 5-th root (α, β)-Metrics with Relatively Isotropic Mean Landsberg Curvature
https://jfga.uma.ac.ir/article_1932.html
In this paper, we study conformally ﬂat 5-th root (&alpha;, &beta;)-metrics. We prove that everyconformally ﬂat 5-th root (&alpha;, &beta;)-metric with relatively isotropic mean Landsberg curvaturemust be either Riemannian metrics or locally Minkowski metrics.On Birecurrent for Some Tensors in Various Finsler Spaces
https://jfga.uma.ac.ir/article_2243.html
The BC&minus; recurrent Finsler space introduced by Alaa et al. [1]. Now in this paper, we introduce and extend BC&minus; birecurrent Finsler space by using some properties of different spaces. We study the relationship between Cartan&rsquo;s second curvature tensor Pijkh and (h)hv torsion tensor Cijk in sense of Berwald. Additionally, the necessary and sufficient condition for some tensors which satisfy birecurrence property will be discuss in different spaces. Four theorems have been established and proved.Reversibility and Sub-reversibility of Finsler Metrics
https://jfga.uma.ac.ir/article_1933.html
In order to extend the sphere theorem for Finsler metrics, the concept of reversibil-ity introduced by H-B. Rademacher for a compact Finsler manifold. In this paper, weextend this notion to the general Finsler manifolds. Then we find an upper bound forthe reversibility of some important spherically symmetric Finsler metrics. Furthermore,we introduce the concept of sub-reversibility for a general Finsler manifold and obtain anon-zero lower bound for this new quantity.ON SPECIAL CLASS OF R-QUADRATIC FINSLER METRICS
https://jfga.uma.ac.ir/article_2244.html
In this paper a special class of R-quadratic generalized $(\alpha, \beta)$-metrics are considered. Some properties of this class are investigated. In special case, the Riemann curvature of this metrics is calculated. Moreover, it is proved that, in this class of metrics, there is not any (non-Riemannian) R-quadratic metrics of non-zero scalar curvature.On the Flag Curvature of Invariant Square Metrics
https://jfga.uma.ac.ir/article_1934.html
In this paper, we give an explicit formula for the flag curvature of invariant square metric and Randers change of square metric.On Square-type Finsler Metrics of Vanishing Flag Curvature
https://jfga.uma.ac.ir/article_1939.html
In this paper, we construct a family of Finsler metrics, called square-type Finsler metrics. We obtain the&nbsp; flag curvature of this metric. Then we&nbsp; find a necessary and sufficient condition under which the&nbsp; flag curvature of square-type Finsler metrics becomes zero.On Projectively Related (α,β)-Metrics
https://jfga.uma.ac.ir/article_1940.html
In this paper, we find necessary and sufficient conditions underwhich the infinite series metric and Randers metric on a manifold M of dimension n &gt;3 be projectively related.General (α, β)-Metrics With Constant Ricci and Flag Curvature
https://jfga.uma.ac.ir/article_1943.html
General (&alpha;, &beta;) metrics form a rich and important class of metrics. Many well-known Finsler metrics of constant flag curvature can be locally expressed as a general (&alpha;, &beta;) metrics. In this paper, we study the general (&alpha;, &beta;) metrics with constant Ricci curvature (tensor) and constant flag curvature. Moreover we study the vanishing non-Riemannian quantity &chi;-curvature.On Einstein Finsler warped product metrics
https://jfga.uma.ac.ir/article_1948.html
In this paper, we study the Finsler warped product metric which is Einstein. We find equation that characterize Einstein Finsler warped product metrics with vanishing Douglas curvature. Moreover, we obtain the differential equation that characterizes Einstein Finsler warped product metrics of locally projectively flat.On the spectral geometry of 4-dimensional Lorentzian Lie group
https://jfga.uma.ac.ir/article_1959.html
The main focus of this paper is concern to the study on the point-wise Osserman structure on 4-dimensional Lorentzian Lie group. In this paper we study on the spectrum of the Jacobi operator and spectrum of the skew-symmetric curvature operator on the non-abelian 4-dimensional Lie group G, whenever G equipped with an orthonormal left invariant pseudo-Riemannian metric g of signature (-;+;+; +), i.e, Lorentzian metric, where e1 is a unit time-like vector. The Lie algebra structure in dimension four has key role in our investigation, also in this case we study on the classification of 1-Stein and mixed IP spaces. At the end we show that G does not admit any space form and Einstein structures.Para-Kähler hom-Lie algebras of dimension 2
https://jfga.uma.ac.ir/article_1960.html
In [12], authors introduced some geometric concepts such as (almost) product, para-complex, para-Hermitian and para-K&auml;hler structures for hom-Lie algebras and they presented an example of a 4-dimensional hom-Lie algebra, which contains these concepts. In this paper, we classify two-dimensional hom-Lie algebras containing these structures. In particular, we show that there doesn't exist para-Kahler proper hom-Lie algebra of dimension 2.