Four families of projectively flat Finsler metrics with \(\mathbf{K}=1\) and their non-Riemannian curvature properties

DOI10.1007/s13398-017-0443-2zbMath1406.53022OpenAlexW2758047711WikidataQ115375821 ScholiaQ115375821MaRDI QIDQ1800642

M. Razgordani, Akbar Tayebi

Publication date: 24 October 2018

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-017-0443-2

zbMATH Keywords

flag curvatureS-curvature\(\Xi\)-curvatureweakly Einstein metricgeneralized 4-th root metriclocally projectively flat metricprojective Ricci curvature

Mathematics Subject Classification ID

Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40)

Related Items (18)

Unnamed Item ⋮ On spherically symmetric Finsler metrics with some non-Riemannian curvature properties ⋮ On non-positively curved homogeneous Finsler metrics ⋮ On conformally flat exponential \((\alpha, \beta)\)-metrics ⋮ On mean Cartan torsion of Finsler metrics ⋮ On recurrent Riemannian and Ricci curvatures of Finsler metrics ⋮ Cheng–Shen conjecture in Finsler geometry ⋮ On Einstein-reversible mth root Finsler metrics ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On conformally flat fourth root \((\alpha,\beta)\)-metrics ⋮ Douglas-Square Metrics with Vanishing Mean Stretch Curvature ⋮ On conformally flat cubic \((\alpha,\beta)\)-metrics ⋮ On homogeneous isotropic Berwald metrics ⋮ A class of Finsler metrics with almost vanishing \(H\)- and \(\Xi\)-curvatures ⋮ On the theory of 4-th root Finsler metrics ⋮ Weighted projective Ricci curvature in Finsler geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized Berwald spaces with \((\alpha, \beta)\)-metrics
• On a class of projectively flat Finsler metrics with flag curvature \(K=1\)
• On generalized \(m\)-th root Finsler metrics
• On \(m\)-th root Finsler metrics
• On \(m\)-th root metrics with special curvature properties
• On generalized Douglas-Weyl \((\alpha, \beta)\)-metrics
• Symplectic geometry and Hilbert's fourth problem
• On Einstein \(m\)-th root metrics
• S-curvature of isotropic Berwald metrics
• Hilbert's fourth problem. I
• Planes for which the lines are the shortest paths between points
• The theory of sprays and Finsler spaces with applications in physics and biology
• Projectively flat Finsler 2-spheres of constant curvature
• S-curvature for a new class of \((\alpha, \beta)\)-metrics
• Über zweidimensionale Finslersche Räume, insbesondere über solche mit geradlinigen Extremalen und positiver konstanter Krümmung. (On two-dimensional Finsler spaces, especially on such with straight line extremal and positive constant curvature)
• Two-dimensional Finsler metrics with constant flag curvature
• Some curvature properties of Cartan spaces with \(m\)th root metrics
• A new class of projectively flat Finsler metrics with constant flag curvature \(K=1\)
• On the classification of projectively flat Finsler metrics with constant flag curvature
• Convergence of two-dimensional trigonometric interpolation polynomials of functions of bounded harmonic variation
• Finsler Metrics of Constant Positive Curvature on the Lie Group S ³
• A note on pseudo-metrics on the plane
• Unicorn metrics with almost vanishing ${ H}$- and ${ \Xi}$-curvatures
• Projectively flat Finsler metrics of constant flag curvature
• Finsler Metrics with K = 0 and S = 0
• On Some Non-Riemannian Quantities in Finsler Geometry
• Generalized P-reducible (α, β)-metrics with vanishing S-curvature
• On a class of locally projectively flat Finsler metrics

This page was built for publication: Four families of projectively flat Finsler metrics with \(\mathbf{K}=1\) and their non-Riemannian curvature properties