文档介绍：Finsler geometry generalizes Riemannian geometry in the same sense that
Banach spaces generalize Hilbert spaces. This book presents an expository
account of seven important topics in Riemann–Finsler geometry, which have
recently undergone significant development but have not had a detailed ped-
agogical treatment elsewhere. Each article will open the door to an active
area of research and is suitable for a special topics course in graduate-level
differential geometry.
Alv´ arez and Thompson discuss the theory of volumes for normed spaces and
Finsler spaces and show how it unifies a wide range of geometric inequalities.
Bellettini studies the evolution of crystals, where the driving agent is the mean
curvature of the facets. Aikou reviews the essential role played by Finsler
metrics plex differential geometry. Chandler and Wong explain why
parametrized jet bundles admit only Finsler metrics and develop machinery
which they use to prove the Kobayashi conjecture (1960) and a special case of
the Green–Griffiths (1979) conjecture. Bao and Robles focus on the flag and
i curvatures of Finsler manifolds, with an emphasis on Einstein metrics
of Randers type. Rademacher gives a detailed and new account of his Sphere
Theorem for nonreversible Finsler metrics. Shen’s article explains why Finsler
manifolds are colorful objects and examines the interplay among the flag, S-,
and Landsberg curvatures in Finsler geometry.
Mathematical Sciences Research Institute
Publications
50
A Sampler of Riemann–Finsler Geometry
Mathematical Sciences Research Institute Publications
1 Freed/Uhlenbeck: Instantons and Four-Manifolds, second edition
2 Chern (ed.): Seminar on Nonlinear Partial Differential Equations
3 Lepowsky/Mandelstam/Singer (eds.): Vertex Operators in Mathematics and Physics
4 Kac (ed.): Infinite Dimensional Groups with Applications
5 Blackadar: K-Theory for Operator Algebras, second edition
6 Moore (ed.): Group Representations, Ergodic Theory, Operato