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Recent developments and some open problems in Finsler geometry. (English) Zbl 1066.53122

Several recent developments and open problems in Finsler geometry are presented. After a brief description of the three classes of geometric invariants on a Finsler space, the authors address the following themes: - the extrinsic geometric invariants for submanifolds in a Finsler manifold; - the harmonic maps between Finsler manifolds and nonlinear spectral theory; - the relations between topological invariants and geometric invariants on Finsler manifolds.

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
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