Riemann Curvature

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

Chapter Chapter 8 in Differential Geometry of Spray and Finsler Spaces, 2001, pp 107-132 from Springer

Abstract: Abstract In 1854, B. Riemann introduced a notion of curvature tensor for Riemannian metrics. Seventy years later (1926), L. Berwald [Bw1][Bw8] successfully extended Riemann’s curvature tensor to Finsler metrics and sprays. In this chapter, we will study the Riemann curvature of Riemannian metrics, Finsler metrics and sprays. Our approach is different from Riemann and Berwald.

Keywords: Covariant Derivative; Local Coordinate System; Ricci Curvature; Ricci Scalar; Riemannian Space (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-9727-2_9

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DOI: 10.1007/978-94-015-9727-2_9

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