Riemann Curvature and Ricci Curvature

Xinyue Cheng () and Zhongmin Shen ()
Additional contact information
Xinyue Cheng: Chongqing University of Technology, School of Mathematics and Statistics
Zhongmin Shen: Indiana University-Purdue University Indianapolis (IUPUI), Department of Mathematical Sciences

Chapter Chapter 4 in Finsler Geometry, 2012, pp 51-59 from Springer

Abstract: Abstract Curvatures are the central concept in geometry. The notion of curvature introduced by B. Riemann faithfully reveals the local geometric properties of a Riemann metric. This curvature is called the Riemann curvature in Riemannian geometry. The Riemann curvature can be extended to Finsler metrics as well as the sectional curvature. In this chapter, we will give a local formula for the Riemann curvature of a Randers metric. Then we shall also study the relationship between the flag curvature and some non-Riemannian geometric quantities.

Keywords: Sectional Curvature; Riemannian Geometry; Ricci Curvature; Riemann Curvature; Finsler Manifold (search for similar items in EconPapers)
Date: 2012
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-24888-7_4

Ordering information: This item can be ordered from
http://www.springer.com/9783642248887

DOI: 10.1007/978-3-642-24888-7_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().