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Finsler Geometry and its Applications - Volume:2 Issue: 1, Aug 2021

Journal of Finsler Geometry and its Applications
Volume:2 Issue: 1, Aug 2021

  • تاریخ انتشار: 1400/05/11
  • تعداد عناوین: 12
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  • Zohre Raei * Pages 1-30
    Let (M, F) be a Finsler manifold and G be the Cheeger-Gromoll metric on TM inducedby F. We show that the curvature tensor field of the Levi-Civita connection on (TM,G) isdetermined by the curvature tensor field of Vrãnceanu connection and some adapted tensorfields on TM. Then we prove that (TM,G) is locally symmetric if and only if (M, F) is locallyEuclidean. Also, we express the flag curvature of the Finsler manifold (M, F).
    Keywords: Finsler manifold, Cheeger-Gromoll metric, Levi-Civita connection, Curvature tensor, Locally symmetric manifold
  • Manoj Kumar * Pages 31-39
    In 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.
    Keywords: Finsler metric, m-th root metric, Matsumoto change, Locally projectively flat metric, Locally dually flat metric
  • Sina Hedayatian *, Neda Izadian, Mohammad Yar Ahmadi Pages 40-50

    In 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.

    Keywords: $(alpha- beta)$, Cartan Torsion, mean Cartan torsion, Landsberg
  • Hassan Sadeghi * Pages 51-62

    The norm of Cartan torsion plays an important role for studying of immersion theory inFinsler geometry. In this paper, we find necessary and sufficient condition under whicha class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifoldhas bounded Cartan torsion.

    Keywords: Finsler metrics, (α -β)-metrics, Cartan Torsion
  • Asmaa Ghasemi * Pages 63-74
    The 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.
    Keywords: L-reducible metric, Randers metric, Landsberg metric
  • Marzeiya Amini * Pages 75-85
    In 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.
    Keywords: cubic metric, (α, β)-metric, Conformally flat metric, relatively isotropic mean Landsberg curvature
  • Mosayeb Zohrehvand * Pages 86-95
    In this paper, we prove that there is not exists non-Riemannian 3-dimensional Berwald manifold with constant main scalars.
    Keywords: Moor frame, weakly Landsberg metric, Landsberg metric, Berwald metric, Randers metric
  • Azadeh Shirafkan * Pages 96-107
    Let 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.
    Keywords: Finsler space, Ricci-quadratic Finsler metric, H-curvature, Anisotropic space-time
  • Shahroud Azami * Pages 108-117
    In 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.
    Keywords: Finsler metric, Ricci-Bourguignon soliton, fundamental group
  • Mehran Gabrani * Pages 118-131
    ‎‎In 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 ‎R‎n‎‎, we prove that it is projectively flat if and only if it is of scalar flag curvature.‎
    Keywords: General spherically symmetric Finsler metrics, projectively flat, flag curvature‎
  • Parastoo Habibi * Pages 132-141
    In 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.
    Keywords: square metric, Geodesic vector, two-step nilpotent Lie group
  • Mehdi Rahimi *, Amir Assari Pages 141-150
    In 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.
    Keywords: Dynamical system, entropy, Riemannian metric