Theory of Finsler spaces with \((\alpha,\beta)\)-metric

DOI10.1016/0034-4877(92)90005-LzbMath0772.53009MaRDI QIDQ2366176

Makoto Matsumoto

Publication date: 29 June 1993

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Finsler geometry

Mathematics Subject Classification ID

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

Related Items (59)

ON HERMITIAN P-COMPLEX FINSLER SPACE WITH SPECIAL (α, β)-METRIC ⋮ On minimal surfaces immersed in three dimensional Kropina Minkowski space ⋮ Generalized Berwald spaces with \((\alpha, \beta)\)-metrics ⋮ \((\alpha_1,\alpha_2)\)-metrics and Clifford-Wolf homogeneity ⋮ On generalized Einstein Randers metrics ⋮ Deforming convex bodies in Minkowski geometry ⋮ The Minkowski norm and Hessian isometry induced by an isoparametric foliation on the unit sphere ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Deformed Infinite series metric in Cartan Spaces ⋮ On spherically symmetric Finsler metrics with some non-Riemannian curvature properties ⋮ On the existence of 3-dimensional Berwald manifolds ⋮ On compact L-reducible Finsler manifolds ⋮ On L-reducible Finsler manifolds ⋮ Invariant vector field on a homogeneous Finsler space with special (α,β)-metric ⋮ Projective vector fields on special (α,β)-metrics ⋮ Unnamed Item ⋮ On the geometry of Randers manifolds ⋮ Finsler geometry for nonlinear path of fluids flow through inhomogeneous media ⋮ Naturally reductive \((\alpha_1, \alpha_2)\) metrics ⋮ Homogeneous Finsler spaces with exponential metric ⋮ On \(L\)-reducible spherically symmetric Finsler metrics ⋮ On locally dually flat \((\alpha,\beta)\)-metrics with isotropic S-curvature ⋮ On Einstein-reversible mth root Finsler metrics ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Invariant Matsumoto metrics on homogeneous spaces ⋮ On the left invariant Randers and Matsumoto metrics of Berwald type on 3-dimensional Lie groups ⋮ ON SEMI-C-REDUCIBILITY OF (α, β)-METRICS ⋮ Constant Curvature Conditions For Generalized Kropina Spaces ⋮ Hypersurfaces of a Finsler space with a special \((\alpha, \beta)\)-metric ⋮ Randers change of \({m^{\mathrm{th}}}\) root metric ⋮ Riemannian and Finslerian geometry in thermodynamics ⋮ Naturally reductive homogeneous space with an invariant \((\alpha,\beta)\)-metric ⋮ On the flag curvature of a homogeneous Finsler sapce with generalized $m$-Kropina metric ⋮ Classes of Finsler spaces with \((\alpha,\beta)\)-metrics ⋮ On Kropina change for \(m\)th root Finsler metrics ⋮ Lagrange spaces with \((y, \beta)\)-metric ⋮ On invariant Matsumoto metrics ⋮ Introduction to Matsumoto metric ⋮ Naturally reductive homogeneous Finsler spaces ⋮ On generalized Douglas-Weyl \((\alpha, \beta)\)-metrics ⋮ Unnamed Item ⋮ Invariant \((\alpha , \beta)\)-metrics on homogeneous manifolds ⋮ On isotropic projective Ricci curvature of C-reducible Finsler metrics ⋮ Naturally reductive homogeneous $(\alpha ,\beta )$-metric spaces ⋮ Unnamed Item ⋮ Time geodesics on a slippery slope under gravitational wind ⋮ Relativistic Finsler geometry ⋮ Homogeneous Finsler spaces with some special $(\alpha, \beta)$-metrics ⋮ On the 1953 Barthel connection of a Finsler space and its mathematical and physical interpretation

Cites Work

• On semi-C-reducibility, T-tensor=0 and S4-likeness of Finsler spaces
• On invariant tensors of \(\beta\)-changes of Finsler metrics
• On conformal transformations of Kropina metric
• The induced and intrinsic Finsler connections of a hypersurface and Finslerian projective geometry
• Finsler geometry, relativity and gauge theories
• Conformal transformation in Finsler spaces with an (\(\alpha\) ,\(\beta\) ) metric
• A slope of a mountain is a Finsler surface with respect to a time measure
• On Finsler geometry of thermodynamical states introduced by R. S. Ingarden
• Projectively flat Finsler spaces with \((\alpha{},\beta{})\)-metric
• On Finsler spaces with Randers' metric and special forms of important tensors
• On Einstein's gravitational field equation in a tangent Riemannian space of a Finsler space
• Motion of the rest frame of the electric charge defined by the Finslerian structure of the electromagnetic field
• On Randers spaces of scalar curvature
• On Finsler spaces with Kropina metric
• On induced and intrinsic connections of Randers' hypersurface
• Contribution to Stephenson-Kilmister’s unified theory of gravitation and elektromagnetism
• Affine field structure of gravitation and electromagnetism
• A unified field theory of gravitation and electromagnetism
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