University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701A new general Finsler connection114100210.22098/jfga.2020.1002ENSalah GomaaElgendiDepartment of Mathematics, Faculty of Science, Benha University, Benha, Egypt. E-mail: salahelgendi@yahoo.comy0000-0002-5808-6092Amr SoleimanDepartment of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt. E-mail:
amrsoleiman@yahoo.com0000-0002-8544-457XAmani AbdelsalamDepartment of Mathematics, Faculty of Science, Benha University, Benha, Egypt. E-mail:
a.m.abdelsalam@fsc.bu.edu.egJournal Article20200212The theory of connections is an important field of research in differential geometry. It was initially developed to solve pure geometrical problems. In the Riemannian contex, M. M. Tripathi introduced a new linear connection on a Riemannian manifold, which generalizes many Riemannian connections such as symmetric, semi-symmetric, qurter-symmetric; Ricci qurter-symmetric; metric, non-metric and recurrent connections. In this paper, we extend the work of M. M. Tripath from Riemannian geometry to Finsler geometry, precisely, we investigate a new linear Finsler connection, which unifies the well known linear connections and provides new connections in Finsler geometry. This connection will be named general linear Finsler (GF-) connection. The existence and uniqueness of such a connection is proved. The curvature and torsion tensors are computed. A general reformulation for Cartan, Berwald, Chern and Hashiguchi connections is obtained. Various special cases and connections are studied and introduced. Moreover, some examples of this connection are studied.https://jfga.uma.ac.ir/article_1002_dba8655e93a1873319bde3411ef0d720.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701Characterization of Finsler spaces of scalar curvature1525100310.22098/jfga.2020.1003ENAmr SoleimanDepartment of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt. E-mail:
amrsoleiman@yahoo.com0000-0002-8544-457XNabil YoussefDepartment of Mathematics, Faculty of Science, Cairo University, Giza, Egypt. E-mail:
nlyoussef2003@yahoo.frJournal Article20200219In Finsler Geometry, all special spaces are investigated locally (using local coordinates) by many authors. On the other hand, the global (or intrinsic, free from local coordinates) investigation of such spaces is very rare in the literature. The aim of the present paper is to provide an intrinsic investigation of two special Finsler spaces whose defining properties are related to Berwald connection, namely, Finsler space of scalar curvature and of constant curvature. Some characterizations of a Finsler space of scalar curvature are proved. Necessary and sufficient conditions under which a Finsler space of scalar curvature reduces to a Finsler space of constant curvature are investigated. It should finally be noted that the present work is formulated in a prospective modern coordinate-free form. Moreover, the outcome of this work is twofold. Firstly, the local expressions of the obtained results, when calculated, coincide with the existing local results. Secondly, new coordinates-free proofs have been established.https://jfga.uma.ac.ir/article_1003_a94dac203e013cc817b38bb563003e75.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701On the geodesics of a homogeneous Finsler space with a special (α, β)−metric2636100610.22098/jfga.2020.1006ENKirandeep KaurDepartment of Mathematics, Punjabi University Constituent College Ghudda, Bathinda, Punjab, India. E-mail:
kirandeepiitd@gmail.comGauree ShankerDepartment of Mathematics and Statistics, School of Basic and Applied Sciences, Central University of Punjab, Bathinda, Punjab, India. E-mail:
gshankar@cup.ac.inJournal Article20200421One of the most important concepts in geometry is of geodesics. Geodesic in a manifold is the generalization of notion of a straight line in an Euclidean space. A geodesic in a homogeneous Finsler space (G/H, F) is called homogeneous geodesic if it is an orbit of a one-parameter subgroup of G. Homogeneous geodesics on homogeneous Riemannian manifolds have been studied by many authors.<br /> Latifi has extended the concept of homogeneous geodesics in homogeneous Finsler spaces. He has given a criterion for characterization of geodesic vectors. Latifi and Razavi have studied homogeneous geodesics in a 3-dimensional connected Lie group with a left invariant Randers metric and show that all the geodesics on spaces equipped with such metrics are homogeneous. <br /> In this paper, first we give basic definitions required to define a honogeneous Finsler space. Next, we study geodesics and geodesic vectors for homogeneous Finsler space with infinite series (α, β)-metric. Next, we give a lemma in which the existence of invariant vector field corresponding to 1-form β for a homogeneous Finsler space with infinite series metric is proved. Further, we find necessary and sufficient condition for a non-zero vector in this homogeneous space to be a geodesic vector.https://jfga.uma.ac.ir/article_1006_11523c969ad8169a2b939ce17a72ace6.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701On H-curvature of Finsler warped product metrics3744100810.22098/jfga.2020.1008ENEsra SevimDepartment of mathematics, Istanbul Bilgi University, Istanbul, Turkey. E-mail:
esra.sengelen@bilgi.edu.trMehran GabraniDepartment of Mathematics, Faculty of Science, Urmia University, Urmia,
Iran. E-mail:
m.gabrani@urmia.ac.irJournal Article20200512In this paper, we study the <strong>H</strong>-curvature, an important non-Riemannian quantity, for a rich and important class of Finsler metrics called Finsler warped product metrics. We find an equation that characterizes the metrics of almost vanishing <strong>H</strong>-curvature. Further, we show that, if F is a Finsler warped product metric, then the <strong>H</strong>-curvature vanishes if and only if the Χ-curvature vanishes. <br /><br /><br /><br /><br /><br /><br />https://jfga.uma.ac.ir/article_1008_8c1565019b3a27b9c1ac90d8b0952e07.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701On generalized symmetric Finsler spaces with some special (α, β)−metrics4553100910.22098/jfga.2020.1009ENMilad Zeinali LakiDepartment of Mathematics, University of Mohaghegh Ardabili, p.o.box. 5619911367, Ardabil-Iran. E-mail:
miladzeinali@hotmail.com0000-0003-2984-4605Journal Article20200624In this paper, we study generalized symmetric Finsler spaces with Matsumoto metric, infinite series metric and exponential metric.The definition of generalized symmetric Finsler spaces is a natural generalization of the definition of Riemannian generalized symmetric spaces. We prove that generalized symmetric (α, β)−spaces with Matsumoto metric, infinite series metric and exponential metric are Riemannian. We also prove that if (M, F) be a generalized symmetric Matsumoto space with F defined by the Riemannian metric a~ and the vector field X, Then the regular s−structure {s<sub>x</sub>} of (M, F) is also a regular s−structure of the Riemannian manifold (M, ã) and if (M, ã) be a generalized symmetric Riemannian space and Also suppose that F is a Matsumoto metric introduced by ã and a vector field X, Then the regular s−structure {s<sub>x</sub>} of (M, ã) is also a regular s−structure of (M, F) if and only if X is s<sub>x</sub>−invariant for all x in M.https://jfga.uma.ac.ir/article_1009_d4821fe491ffb86bdf0fe6ab01cb80fa.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701On generalized 4-th root Finsler metrics5459101010.22098/jfga.2020.1010ENTayebeh TabatabaeifarDepartment of Mathematics and Computer Science, Amirkabir University of
Technology (Tehran Polytechnic), Tehran. Iran.
E-mail: t.tabatabaeifar@aut.ac.ir0000-0002-5334-0135Journal Article20200828In this paper, we prove that every generalized cubic Finsler metric with vanishing Landsberg curvature is a Berwald metric. This yields an extension of Matsumoto theorem for the cubic metric. Then, we show that every generalized 4-th root Finsler metric with vanishing Landsberg curvature is a Berwald metric.https://jfga.uma.ac.ir/article_1010_d6508b8baf1032771afdc7c9bf6b9d3c.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701A special class of Finsler metrics6065101110.22098/jfga.2020.1011ENHassan SadeghiDepartment of Mathematics, Faculty of Science, University of Qom,
Qom. Iran.
E-mail: sadeghihassan64@gmail.comJournal Article20200828In this paper, we study a special class of Finsler metrics F = F(x, y) in R<sup>n</sup> that satisfy F(−x, y) = F(x, y). We show the induced distance function of F satisfies d<sub>F</sub> (p, q) = d<sub>F</sub> (−q,−p) for all p, q in R<sup>n</sup>. The geodesics of these metrics have special property and many well-known Finsler metrics belong to this class. We prove that these metrics with constant S-curvature satisfy <strong>S</strong> = 0.https://jfga.uma.ac.ir/article_1011_37714c7f5e76e47612edc55a6af0e38d.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701On the norm of Cartan torsion of two classes of (α, β)−metrics6672101210.22098/jfga.2020.1012ENTahere RajabiDepartment of Mathematics, Faculty of Science, University of Qom,
Qom. Iran
E-mail: tr rajabi@yahoo.comJournal Article20200906Z. Shen proved that Finsler manifold with unbounded Cartan torsion can not be isometrically imbedded into any Minkowski space. This shows that the norm of Cartan torsion of Finsler metrics has an essential role for studying of immersion theory in Finsler geometry. In this paper, we study the norm of Cartan torsion of Ingarden-Tàmassy and Arctangent Finsler metrics that are special (α, β)-metrics.https://jfga.uma.ac.ir/article_1012_d59ab3164b96df43e5fb7431aa1395eb.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701The class of Matsumoto metrics with almost vanishing H-curvatures7383101310.22098/jfga.2020.1013ENMorteza FaghfouriDepartment of Pure Mathematics, Faculty of Mathematical Sciences,
University of Tabriz,
Tabriz, Iran. Email: faghfouri@tabrizu.ac.ir0000-0003-3041-8777Nadereh JazerDepartment of Pure Mathematics, Faculty of Mathematical Sciences,
University of Tabriz,
Tabriz, Iran. Email: njazer@tabrizu.ac.irJournal Article20200829In this paper, we are going to consider a class of (α, β)-metrics which introduced by Matsumoto. We find a condition under which a Matsumoto metric of almost vanishing <strong>H</strong>-curvature reduces to a Berwald metric.https://jfga.uma.ac.ir/article_1013_008054b8fb0212ecda374f80677c70f5.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701Characterization of the Killing and homothetic vector fields on Lorentzian pr-waves three-manifolds with recurrent curvature8488101410.22098/jfga.2020.1014ENParvane AtashpeykarDepartment of mathematics, Basic science faculty, University of Bonab,
Bonab, Iran. Email: p.atashpeykar@bonabu.ac.irAli Haji-BadaliDepartment of mathematics, Basic science faculty, University of Bonab,
Bonab, Iran. Email: haji.badali@ubonab.ac.ir0000-0001-5309-5902Journal Article20200914We consider the Lorentzian pr-waves three-manifolds with recurrect curvature. We obtain a full classification of the Killing and homothetic vector fields of these spaces.https://jfga.uma.ac.ir/article_1014_c2325cf1351e247e819912abb05f3cf5.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701Homogeneous geodesics in homogeneous Randers spaces - examples8995101510.22098/jfga.2020.1015ENParastoo HabibiDepartment of Mathematics, Islamic Azad University, Astara branch,
Astara, Iran.
E-mail: p.habibi@iau-astara.ac.irJournal Article20200915In this paper, we study homogeneous geodesics in homogeneous Randers spaces. we give a four dimensional example and we obtain homogeneous geodesics of this space in some special cases.https://jfga.uma.ac.ir/article_1015_a9ac7c222eaade9ff2183a008005a6f4.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001120200701Characterization of 3-dimensional left-invariant locally projectively flat Randers metrics96102101610.22098/jfga.2020.1016ENMona AtashafrouzFaculty of Mathematics and Computer Sciences, Amirkabir University of
Technology (Tehran Polytechnic), Tehran. Iran.
E-mail: m.atashafrooz@aut.ac.irJournal Article20201027In this paper, we characterize locally projectively flat left-invariant Randers metrics on simply connected three dimensional Lie groups.https://jfga.uma.ac.ir/article_1016_00ae4dec05c9adf8d614a85892741403.pdf