University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701On the geometry of tangent bundle of Finsler manifold with Cheeger-Gromoll metric130126010.22098/jfga.2021.1260ENZohre RaeiDepartment of Mathematics, Faculty of Science,
University of Mohaghegh Ardabili,
Ardabil, Iran. Email: raei.zohre@gmail.comJournal Article20210805Let (M, F) be a Finsler manifold and G be the Cheeger-Gromoll metric on TM induced<br />by F. We show that the curvature tensor field of the Levi-Civita connection on (TM,G) is<br />determined by the curvature tensor field of Vrãnceanu connection and some adapted tensor<br />fields on TM. Then we prove that (TM,G) is locally symmetric if and only if (M, F) is locally<br />Euclidean. Also, we express the flag curvature of the Finsler manifold (M, F).https://jfga.uma.ac.ir/article_1260_e9f54721348b6e5779406872b1f5d1c4.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701Locally dually flatness and locally projectively flatness of Matsumoto change with m-th root Finsler metrics3139126110.22098/jfga.2021.1261ENManoj KumarDepartment of Mathematics and Stataistics, Faculty of Science,
Dr. Rammanohar Lohia Avadh University,
Ayodhya-224001, India.
E-mail: mvermamath@gmail.com and mkvermabhu1986@gmail.com0000-0002-8523-3430Journal Article20210724In this paper, we study the Matsumoto change of m-th root Finsler metric. We find the necessary and sufficient conditions under which the transformed metric be locally dually flat. Also, we prove that for Matsumoto change of m-th root metric is locally projectively flat if and only if it is locally Minkowskian.https://jfga.uma.ac.ir/article_1261_dcad6897e0a34aefa37e0df2ebfa0bcd.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701A class of Finsler metrics with bounded non-Riemannian curvatures4050126210.22098/jfga.2021.1262ENSina HedayatianDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz-Iran. Email: hedayatian@scu.ac.irNeda IzadianDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz-Iran. Email: nezadiyan@gmail.comMohammad Yar AhmadiDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz-Iran. Email: m.yarahmadi@scu.ac.irJournal Article20210726In this paper, we find a necessary and sufficient condition for a class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifold which has bounded mean Cartan torsion. Moreover, we obtain a necessary and sufficient condition under which the above mentioned class of Finsler metrics has bounded mean Landsberg curvature. Next, we investigate these metrics with bounded mean Cartan torsion and mean Landsberg curvature. Furthermore, we give explicit examples of this type of metrics.https://jfga.uma.ac.ir/article_1262_a71248f243d0ce03efc06f0ed403ccfc.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701Finsler metrics with bounded Cartan torsion5162126310.22098/jfga.2021.1263ENHassan SadeghiDepartment of Mathematics,
Faculty of Science,
University of Qom, Qom, Iran
E-mail: sadeghihassan64@gmail.comJournal Article20210727The norm of Cartan torsion plays an important role for studying of immersion theory in<br />Finsler geometry. In this paper, we find necessary and sufficient condition under which<br />a class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifold<br />has bounded Cartan torsion.https://jfga.uma.ac.ir/article_1263_e7ded6dad95a0ffa18fa91d3aa0bed79.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701On compact L-reducible Finsler manifolds6374126410.22098/jfga.2021.1264ENAsmaa GhasemiDepartment of Mathematics,
Faculty of Science,
University of Hormozgan
Bandar-Abbas, Iran
E-mail: ghasemi.asmaa@gmail.comJournal Article20210801The class of L-reducible Finsler metric was introduced by Matsumoto as a generalization of Randers metrics. One open problems in Finsler Geometry is to find a L-reducible metric which is not of Randers-type. Let (M,F) be a compact 3-dimensional L-reducible metric. Suppose that F has constant relatively isotropic mean Landsberg curvature. Then we show that F reduces to a Randers metric.https://jfga.uma.ac.ir/article_1264_7663b0c14911dc6aff96d975151f17e4.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701On conformally flat cubic (α, β)-metrics7585126510.22098/jfga.2021.1265ENMarzeiya AminiDepartment of Mathematics, Faculty of Science,
University of Qom, Qom. Iran
E-mail: marzeia.amini@gmail.comJournal Article20210731In this paper, we study the class of conformally flat cubic (α, β)-metrics. We prove that every conformally flat cubic (α, β)-metric with relatively isotropic mean Landsberg curvature must be either Riemannian metrics or locally Minkowski metrics.https://jfga.uma.ac.ir/article_1265_ea2ea15a25a45d6a4ed7ece014dfb633.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701On the existence of 3-dimensional Berwald manifolds8695126610.22098/jfga.2021.1266ENMosayeb ZohrehvandDepartment of Mathematical Science, Faculty of Mathematical Science and Statistics, Malayer University, Malayer, Iran. Email: m.zohrehvand@malayeru.ac.ir0000-0002-3876-4060Journal Article20210804In this paper, we prove that there is not exists non-Riemannian 3-dimensional Berwald manifold with constant main scalars.https://jfga.uma.ac.ir/article_1266_db5b40348f88695508e1df200367be65.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701On a class of Ricci-quadratic Finsler metrics96107126710.22098/jfga.2021.1267ENAzadeh ShirafkanDepartment of Mathematics, Faculty of Mathematical Sciences,
University of Mazandaran, Babolsar, Iran
E-mail: ashirafkan@umz.ac.irJournal Article20210805Let F be a (reversible) Finsler metric on a Riemannian space (M, α) of positive (or negative) sectional curvature. Suppose that the Ricci curvature of F is horizontally constant along Finslerian geodesics. Then we show that F is a Ricci-quadratic Finsler metric.https://jfga.uma.ac.ir/article_1267_f8f3f249f04c1a53a5a0c1c7861240be.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701Complete Ricci-Bourguignon solitons on Finsler manifolds108117126810.22098/jfga.2021.1268ENShahroud AzamiDepartment of Pure Mathematics, Faculty of Science,
Imam Khomeini International University,
Qazvin, Iran.
E-mail: azami@sci.ikiu.ac.ir, shahrood78@gmail.com0000-0002-8976-2014Journal Article20210809In this paper, we study Ricci-Bourguignon soliton on Finsler manifolds and prove any forward complete shrinking Finslerian Ricci-Bourguignon soliton under some conditions on vector filed and scalar curvature is compact and its fundamental group is finite.https://jfga.uma.ac.ir/article_1268_389e9603b2f395c8f1f023d46db8eca1.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701On a class of Finsler metrics of scalar flag curvature defined by the Euclidean metric and related 1-forms118131126910.22098/jfga.2021.1269ENMehran GabraniDepartment of Mathematics, Faculty of Science,
Urmia University, Urmia, Iran.
E-mail: m.gabrani@urmia.ac.irJournal Article20210809In this paper, we study a class of Finsler metrics called general spherically symmetric Finsler metrics which are defined by the Euclidean metric and related 1-forms. For a class of the metrics in R<sup>n</sup>, we prove that it is projectively flat if and only if it is of scalar flag curvature.https://jfga.uma.ac.ir/article_1269_be3a34ab972260360d2d959486b38ae8.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701Geodesic vectors of invariant square metrics on nilpotent Lie groups of dimension five132141127010.22098/jfga.2021.1270ENParastoo HabibiDepartment of Mathematics, Islamic Azad University,
Astara branch, Astara, Iran.
E-mail: p.habibi@iau-astara.ac.irJournal Article20210808In this paper we consider invariant square metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces. We study geodesic vectors and investigates the set of all homogeneous geodesics on two-step nilpotent Lie groups of dimension five.https://jfga.uma.ac.ir/article_1270_a1f6ca042f06df813497fad54817a2dd.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05002120210701A note on entropy of finitely ergodic compact topological dynamical systems142150127110.22098/jfga.2021.1271ENMehdi RahimiDepartment of Mathematics, Faculty of Science,
University of Qom, Qom, Iran.
E-mail: m10.rahimi@gmail.comAmir AssariDepartment of Basic Science, Jundi-Shapur University of Technology,
Dezful, Iran.
E-mail: amirassari@jsu.ac.irJournal Article20210810In this paper, using a map on the product space, we define a linear functional on a Hilbert space and we extract the metric entropy of a system as the operator norm of the linear functional. This follows an approach which considers the entropy of a dynamical system as a linear operator.https://jfga.uma.ac.ir/article_1271_0e2e55a66327bafc9bf8b3f27e98b244.pdf