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Riemann Curvature and Ricci Curvature [PDF]

open access: possible, 2012
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.
Xinyue Cheng, Zhongmin Shen
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Structural curvature versus amplitude curvature

The Leading Edge, 2011
Because they are second-order derivatives, seismic curvature attributes can enhance subtle information that may be difficult to see using first-order derivatives such as the dip magnitude and the dip-azimuth attributes. As a result, these attributes form an integral part of most seismic interpretation projects.
Kurt J. Marfurt, Satinder Chopra
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Solitons of curvature

Acta Applicandae Mathematicae, 1995
An intristic geometry of surfaces is discussed. In geodesic coordinates the Gauss equation is reduced to the Schrodinger equation where the Gaussian curvature plays the role of a potential. The use of this fact provides an infinite set of explicit expressions for the curvature and metric of a surface.
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Douglas Curvature and Weyl Curvature

2001
There are two important projective invariants of sprays and Finsler metrics. One is a non-Riemannian projective invariant constructed from the Berwald curvature. The other is a Riemannian projective invariant constructed from the Riemann curvature. In this chapter, we will discuss these two projective invariants.
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Curvature of Surfaces [PDF]

open access: possible, 2001
In this chapter, we discuss several approaches to the problem of measuring how ‘curved’ a surface is. Although they use quite different methods, we show that each of the approaches leads to the same geometric object: the second fundamental form of a surface.
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