Contents Foreword ............................................................... vii Paul Finsler and friends ............................................... ix Section 1 Finsler Geometry over the Reals 0. Preface ................................................................ 3 1. D. Bao, S.S. Chern and Z. Shen: On the Gauss-Bonnet integrand for 4-dimensional Landsberg spaces ... 15 2. R. Bryant: Finsler structures on the 2-sphere satisfying K = 1 .................... 27 3. G.D. Chakerian: Integral geometry in Minkowski spaces ................................ 43 4. S.S. Chern: Riemannian geometry as a special case of Finsler geometry ............ 51 5. F.J. Flaherty: Dirac operators for Finsler spaces ..................................... 59 6. D. Bao and B. Lackey: Special eigenforms on the sphere bundle of a Finsler manifold .......... 67 7. M. Matsumoto: Remarks on Berwald and Landsberg spaces ............................ 79 8. Z. Shen: Finsler manifolds of constant positive curvature ....................... 83 Section 2 Complex Finsler Geometry 0. Preface ............................................................... 97 1. M. Abate and G. Patrizio: Finsler metrics of constant curvature and the characterization of tube domains ............................. 101 2. T. Aikou: Some remarks on locally conformal complex Berwald spaces .......... 109 3. J. Bland and M. Kalka: Variations of holomorphic curvature for Kahler Finsler metrics ....... 121 4. J. Faran: The equivalence problem for complex Finsler Hamiltonians ........... 133 5. S. Kobayashi: Complex Finsler vector bundles ...................................... 145 v
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