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Structure Equations of Sprays

In: Differential Geometry of Spray and Finsler Spaces

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  • Zhongmin Shen

    (Indiana University-Purdue University at Indianapolis, Department of Mathematical Sciences)

Abstract

Sprays are special vector fields on the tangent bundle. All of the quantities defined by a spray live on the tangent bundle. In previous chapters, we treat them as quantities on the base manifold by choosing a reference vector. To find the internal relationship among various quantities such as the Berwald curvature, Landsberg curvature and Riemann curvature, etc., one has to go up to the tangent bundle. It seems that exterior differential method is quite useful in computation for this purpose. We will employ it to do some complicated computations.

Suggested Citation

  • Zhongmin Shen, 2001. "Structure Equations of Sprays," Springer Books, in: Differential Geometry of Spray and Finsler Spaces, chapter 0, pages 133-142, Springer.
    • Handle: RePEc:spr:sprchp:978-94-015-9727-2_10
    DOI: 10.1007/978-94-015-9727-2_10
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