The Differential Geometry of Finsler Spaces

1. Front Matter

   Pages II-XV

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2. Calculus of Variations. Minkowskian Spaces

   • Hanno Rund

   Pages 1-43

3. Geodesics: Covariant Differentiation

   • Hanno Rund

   Pages 44-64

4. The “Euclidean Connection” of E. Cartan

   • Hanno Rund

   Pages 65-93

5. The Theory of Curvature

   • Hanno Rund

   Pages 94-149

6. The Theory of Subspaces

   • Hanno Rund

   Pages 150-214

7. Miscellaneous Topics

   • Hanno Rund

   Pages 215-262

8. Back Matter

   Pages 262-284

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The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry. Secondly, it is hoped that this monograph may serve also as an introduction to a branch of differential geometry which is closely related to various topics in theoretical physics, notably analytical dynamics and geometrical optics. With this second object in mind, an attempt has been made to describe the basic aspects of the theory in some detail - even at the expense of conciseness - while in the more specialised sections of the later chapters, which might be of interest chiefly to the specialist, a more succinct style has been adopted. The fact that there exist several fundamentally different points of view with regard to Finsler geometry has rendered the task of writing a coherent account a rather difficult one. This remark is relevant not only to the development of the subject on the basis of the tensor calculus, but is applicable in an even wider sense. The extensive work of H. BUSEMANN has opened up new avenues of approach to Finsler geometry which are independent of the methods of classical tensor analysis. In the latter sense, therefore, a full description of this approach does not fall within the scope of this treatise, although its fundamental l significance cannot be doubted.

• Finsler geometry
• Tensor
• calculus
• differential geometry
• geometry
• tensor analysis

• The University of Natal, Brazil

  Hanno Rund

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