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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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Programming curvature using origami tessellations.
Nature Materials, 2016Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes.
Levi H. Dudte +3 more
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Mixed-curvature Variational Autoencoders
International Conference on Learning Representations, 2019Euclidean geometry has historically been the typical "workhorse" for machine learning applications due to its power and simplicity. However, it has recently been shown that geometric spaces with constant non-zero curvature improve representations and ...
Ondrej Skopek, O. Ganea, Gary B'ecigneul
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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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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
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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, 2017
We describe the history, guiding mechanism, recent advances, applications, and future prospects for hollow-core negative curvature fibers. We first review one-dimensional slab waveguides, two-dimensional annular core fibers, and negative curvature tube ...
Chengli Wei +3 more
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We describe the history, guiding mechanism, recent advances, applications, and future prospects for hollow-core negative curvature fibers. We first review one-dimensional slab waveguides, two-dimensional annular core fibers, and negative curvature tube ...
Chengli Wei +3 more
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Metric Inequalities with Scalar Curvature
Geometric and Functional Analysis, 2017We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below. In so far as geometry is concerned these inequalities appear as generalisations of the classical bounds on ...
M. Gromov
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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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