University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201Invariant vector field on a homogeneous Finsler space with special (α,β)-metric114123510.22098/jfga.2020.1235ENMahnaz EbrahimiDepartment of Mathematics, University of Mohaghegh Ardabili,
Ardabil, Iran
E-mail: m.ebrahimi@uma.ac.irJournal Article20210119In a Finsler spaces, we consider a special (α,β)-metric L satisfying L<sup>2</sup>(α,β) =<br />c<sub>1</sub> α <sup>2</sup> +2c<sub>2</sub> αβ+c<sub>3</sub>β<sup>2</sup>, where c<sub>i</sub> are constant. In this paper, the existence of invariant vector<br />elds on a special homogeneous (α,β)-space with L metric is proved. Then we study geodesic<br />vectors and investigate the set of all homogeneous geodesics of invariant (α,β)-metric L on<br />homogeneous spaces and simply connected 4-dimensional real Lie groups admitting invariant<br />hypercomplex structure.https://jfga.uma.ac.ir/article_1235_9d2d00e444a73400bb44984776920e33.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201Douglas (α,β)-metrics on four-dimensional nilpotent Lie groups1526123610.22098/jfga.2020.1236ENHamid Reza Salimi MoghaddamDepartment of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441-Iran. Email: salimi.moghaddam@gmail.com0000-0001-6112-4259Hossein Abedi KarimiDepartment of Mathematics,
Isfahan University of Technology, Isfahan, 84156-83111-Iran. Email:hossein.abedikarimi@gmail.comMehri NasehiFaculty of Basic Sciences,
University of Shahreza, P. O. Box: 86149-
56841, Shahreza, Iran. Email: nasehi.mehri@gmail.comJournal Article20210411In this paper, we give a classification of left-invariant Douglas and Berwald (α,β)-metrics on simply connected four-dimensional nilpotent Lie groups. We show that there are not any bi-invariant Randers metrics on four-dimensional nilpotent Lie groups. Then, we explicitly give the flag curvature formulas and geodesic vectors of these spaces. Finally, we give the formula of <strong>S</strong>-curvature of left-invariant Randers metrics of Douglas type.https://jfga.uma.ac.ir/article_1236_d6196ed57df3d67c5c223c569dc3bda1.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201IFP transformations on the cotangent bundle with the modified Riemannian extension2738123710.22098/jfga.2020.1237ENMosayeb ZohrehvandDepartment of Mathematical Science and Statistics, Malayer University, Malayer, Iran. Email: m.zohrehvand@malayeru.ac.ir0000-0002-3876-4060Journal Article20210101Let ∇ be a symmetric connection on an n-dimensional manifold M <sub>n</sub><br />and T <sup>∗</sup> M n its cotangent bundle. In this paper, firstly, we determine the<br />infinitesimal fiber-preserving projective(IFP) transformations on T <sup>∗</sup> M <sub>n</sub><br />with respect to the Riemannian connection of the modified Riemannian<br />extension <sup>˜</sup> g ∇<sub>,c</sub> where c is a symmetric (0,2)-tensor field on M<sub> n</sub> . Then<br />we prove that, if (T <sup>∗</sup> M <sub>n</sub> , <sup>˜</sup> g ∇<sub>,c</sub> ) admits a non-affine infinitesimal fiber-<br />preserving projective transformation, then M n is locally flat, where ∇<br />is the Levi-Civita connection of a Riemannian metric g on M <sub>n</sub> . Finally,<br />the infinitesimal complete lift, horizontal and vertical lift projective trans-<br />formations on (T <sup>∗</sup> M <sub>n</sub> ,<sup> ˜</sup> g ∇<sub>,c</sub> ) are studied.https://jfga.uma.ac.ir/article_1237_72b2d06af7c5c765d2445eff11c74e51.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201On projectively related spherically symmetric metrics in Finsler geometry3953123810.22098/jfga.2020.1238ENHassan SadeghiFaculty of Science, Department of Mathematics
University of Qom, Qom, Iran
E-mail: sadeghihassan64@gmail.comMorad BahadoriFaculty of Science, Department of Mathematics
University of Qom,
Qom, Iran. Email: E-mail: moradbahadori3@gmail.comJournal Article20210507Inspired by the notion of projectively related spherically symmetric metrics, we study the class of Finsler metrics whose geodesics have the same shape with a difference in rotation or reflection of their graphs. This class of metrics contains the class of projectively related Finsler metrics. First, we characterize the class of Randers metrics, ( α, β )-metrics and spherically symmetric metrics in this class of metricshttps://jfga.uma.ac.ir/article_1238_9a4ce0f84982426f2f4e2c33f2c86e9f.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201On projectively flat Finsler warped product metrics with isotropic E-curvature5462123910.22098/jfga.2020.1239ENMehran GabraniDepartment of Mathematics, Faculty of Science,
Urmia University, Urmia, Iran.
Email: m.gabrani@urmia.ac.irEsra Sengelen SevimDepartment of Mathematics, Istanbul Bilgi University, 34060, Eski
Silahtaraga Elektrik Santrali, Kazim Karabekir Cad.
No: 2/13 Eyupsultan, Istanbul, Turkey.
E-mail: esra.sengelen@bilgi.edu.trJournal Article20210717In this paper, we study a special class of Finsler metrics F= α∅(r, s) called warped product metrics where α is a Riemannian metric, r= u<sup>1</sup> and s= v<sup>1</sup>/α. We show that every projectively flat Finsler warped product metrics with isotropic <strong>E</strong>-curvature is a Randers metric.https://jfga.uma.ac.ir/article_1239_3801f5b936456b6b897e78981b935ca2.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201On weakly Landsberg 3-dimensional Finsler Spaces6372124010.22098/jfga.2020.1240ENMarzeiya AminiDepartment of Mathematics, Faculty of science, University of Qom. Email: marzeia.amini@gmail.comJournal Article20210702In this paper, we study the class of 3-dimensional Finsler manifolds. We find the necessary and sufficient condition under which a 3-dimensional weakly Landsberg metric reduces to a Landsberg metric.https://jfga.uma.ac.ir/article_1240_569211e986d39d1fbefb2a29969fb30c.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201On L-reducible Finsler manifolds7382124110.22098/jfga.2020.1241ENSareh BeizaviSchool of Mathematics, Iran University of Science and Technology,
Narmak, Tehran, 16846 -13114, Iran
E-mail: h beizavi@mathdep.iust.ac.irJournal Article20210704In this paper, we consider the class of L-reducible Finsler metrics which contains the class of C-reducible metrics and the class of Landsberg metrics. Let (M,F) be a 3-dimensional L-reducible Finsler manifold. Suppose that F has a relatively isotropic mean Landsberg curvature. We find a condition on the main scalars of F under which it reduces to a Randers metric or a Landsberg metric.https://jfga.uma.ac.ir/article_1241_36e1e8e976b7ff7587a942051272ab7b.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201Projective vector fields on special (α,β)-metrics8393124210.22098/jfga.2020.1242ENSaeedeh MasoumiDepartment of Mathematics, Faculty of Science,
Urmia University, Urmia, Iran.
E-mail: s.masoumi94@gmail.comJournal Article20210725In this paper, we study the projective vector fields on two special<br />(α,β)-metrics, namely Kropina and Matsumoto metrics. First, we consider<br />the Kropina metrics, and show that if a Kropina metric F = α<sup>2</sup>/β admits<br />a projective vector field, then this is a conformal vector field with respect to<br />Riemannian metric a or F has vanishing S-curvature. Then we study the<br />Matsumoto metric F = α<sup>2</sup>/(α−β) and prove that if the Matsumoto metric<br />F = α<sup>2</sup>/β admits a projective vector field, then this is a conformal vector field<br />with respect to Riemannian metric a or F has vanishing <strong>S</strong>-curvature.https://jfga.uma.ac.ir/article_1242_acc3899280480efa9b03c9e4c2609266.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201On semi-P-reducible Finsler manifolds with relatively isotropic Landsberg curvature94104124310.22098/jfga.2020.1243ENMorteza FaghfouriDepartment of Pure Mathematics,
Faculty of Mathematical Sciences,
University of Tabriz
Tabriz. Iran
E-mail: faghfouri@tabrizu.ac.ir0000-0003-3041-8777Journal Article20210709The class of semi-P-reducible Finsler metrics is a rich and basic class of Finsler metrics that contains the class of L-reducible metrics, C-reducible metrics, and Landsberg metrics. In this paper, we prove that every semi-P-reducible manifold with isotropic Landsberg curvature reduces to semi-C-reducible manifolds. Also, we prove that a semi-P-reducible Finsler metric of relatively isotropic mean Landsberg curvature has relatively isotropic Landsberg curvature if and only if it is a semi-C-reducible Finsler metric.https://jfga.uma.ac.ir/article_1243_8826cb982805e16ad74aceef25e1facc.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201The algebraic Ricci soliton of Lie groups H2×R and Sol_3105114124410.22098/jfga.2020.1244ENParvane AtashpeykarDepartment of Mathematics, Basic Sciences Faculty,
University of Bonab, Bonab 5551395133, Iran.
E-mail: p.atashpeykar@ubonab.ac.irAli Haji-BadaliDepartment of Mathematics, Basic Sciences Faculty,
University of Bonab, Bonab 5551395133, Iran.
E-mail: haji.badali@ubonab.ac.ir0000-0001-5309-5902Journal Article20210721In this article, we study the algebraic Ricci solitons of three-dimensional Lie group H<sup>2</sup>×R, endowed with a left-invariant Riemannian metric. Also, we examine the existence of sol-solitons on the three-dimensional Lie group Sol<sub>3</sub>, endowed with a left-invariant Riemannian metric.https://jfga.uma.ac.ir/article_1244_be99685bc56d6cd56baa19d4cb2bf36e.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201On the locally flat Finsler manifolds115129124510.22098/jfga.2020.1245ENSeiedeh Sedigheh AlaviDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran. Email: sedighehalavi54@gmail.comJournal Article20210722It is proved that every locally flat Finsler manifold is a locally flat Riemannian manifold. Some low dimensional locally Finsler manifolds are classified. It is also proved that in a categorical sense, there is a correspondence between locally flat Finsler manifolds and locally hessian Riemannian manifoldshttps://jfga.uma.ac.ir/article_1245_28136f81fc7aadef8127f9c8468d6837.pdfUniversity of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05001220201201On semi C-reducible Finsler spaces130142124610.22098/jfga.2020.1246ENAbbas HeydariDepartment of Pure Mathematics,
Faculty of Mathematical Sciences, Tarbiat Modares University,
Tehran, Iran
E-mail: aheydari@modares.ac.irJournal Article20210712In this paper, we study the class of semi-C-reducible Finsler manifolds. Under a condition, we prove that every semi-C-reducible Finsler spaces with a semi-P-reducible metric has constant characteristic scalar along Finslerian geodesics or reduces to a Landsberg metric. By this fact, we characterize the class of semi-P-reducible spaces equipped with an (α, β)-metric. More precisely, we proved that such metrics are Berwaldian B= 0,or have vanishing S-curvature S= 0 or satisfy a well-known ODE. This yields an extension of Tayebi-Najafi’s classification for 3-dimensional (α, β)-metric of Landsberg-type.https://jfga.uma.ac.ir/article_1246_ab56439a0afbfde0c3c80bf897a6623a.pdf