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Ricci Curvature Tensor and Non-Riemannian Quantities

Published online by Cambridge University Press:  20 November 2018

Benling Li  and
Zhongmin Shen
Benling Li
Affiliation:
Department of Mathematics, Ningbo University, Ningbo, Zhejiang Province 315211, P.R. China e-mail: libenling@nbu.edu.cn
Zhongmin Shen
Affiliation:
Department of Mathematical Sciences, Indiana University-Purdue University, Indianapolis, IN 46202-3216, US e-mail: zshen@math.iupui.edu
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Abstract

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There are several notions of Ricci curvature tensor in Finsler geometry and spray geometry. One of them is defined by the Hessian of the well-known Ricci curvature. In this paper we will introduce a new notion of Ricci curvature tensor and discuss its relationship with the Ricci curvature and some non-Riemannian quantities. Using this Ricci curvature tensor, we shall have a better understanding of these non-Riemannian quantities.

Keywords

53B4053C60Finsler metricsspraysRicci curvaturenon-Riemanian quantity
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 3 , 01 September 2015 , pp. 530 - 537
Copyright
Copyright © Canadian Mathematical Society 2015

References

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