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On the Curvatures of a Surface
American Journal of Mathematics, 19531. The smoothness of H and K. A point set 8 in the (x, y, z) -space is said to be a (small piece of a) surface of class Gn, where n ^ 1, if it is the locus of the endpoints of a vector function X = X(u,v) with three com? ponents which is defined on a two-dimensional (u, v) -domain, possesses con?
Aurel Wintner, Philip Hartman
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Acta Applicandae Mathematicae, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Riemann Curvature and Ricci Curvature [PDF]
, 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, 2011Because 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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Oberwolfach Reports, 2005
It was the aim of the meeting to bring together international experts from the theory of buildings, differential geometry and geometric group theory. Buildings are combinatorial structures (simplicial complexes) which can be seen as simultaneously generalizing projective spaces and trees.
Bertrand Rémy +3 more
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It was the aim of the meeting to bring together international experts from the theory of buildings, differential geometry and geometric group theory. Buildings are combinatorial structures (simplicial complexes) which can be seen as simultaneously generalizing projective spaces and trees.
Bertrand Rémy +3 more
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The Annals of Mathematics, 1970 The theorema egregium or, in essence, the fundamental theorem of riemannian geometry asserts that curvature is an invariant of the metric. We ask the converse: how far does curvature determine the metric? Important theorems in this direction are the classical theorems for (embedded) surfaces. More recently there is a local theorem of E.
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, 1997 If you’ve just completed an introductory course on differential geometry, you might be wondering where the geometry went. In most people’s experience, geometry is concerned with properties such as distances, lengths, angles, areas, volumes, and curvature.
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Douglas Curvature and Weyl Curvature
2001There 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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, 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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