Results 231 to 240 of about 26,863 (267)
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Acta Applicandae Mathematica, 2001
This paper is the new section 5 of the author's paper ``Affine connection complexes'', which appeared ibid. 59, 215-227 (1999; Zbl 0956.53014). Here is given the proof of Proposition 5.4.: The Riemannian curvature tensor \(R(g)\in\otimes^4\varepsilon\) of any Riemannian manifold \((M,g)\) is a symmetric element of the submodule \(A^2\varepsilon\otimes ...
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This paper is the new section 5 of the author's paper ``Affine connection complexes'', which appeared ibid. 59, 215-227 (1999; Zbl 0956.53014). Here is given the proof of Proposition 5.4.: The Riemannian curvature tensor \(R(g)\in\otimes^4\varepsilon\) of any Riemannian manifold \((M,g)\) is a symmetric element of the submodule \(A^2\varepsilon\otimes ...
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General Relativity and Gravitation, 1999
Translation from the German of Z. Phys. 10, 377--386 (1922; JFM 48.1031.02).
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Translation from the German of Z. Phys. 10, 377--386 (1922; JFM 48.1031.02).
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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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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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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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SIAM Journal on Applied Mathematics, 1970
Upper and lower approximations on certain definite integrals are used in this paper to obtain the maximum length of a smooth curve satisfying certain side conditions, including specified minimum radius of curvature. The question has appeared (and was unresolved) in at least two previous research publications.
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Upper and lower approximations on certain definite integrals are used in this paper to obtain the maximum length of a smooth curve satisfying certain side conditions, including specified minimum radius of curvature. The question has appeared (and was unresolved) in at least two previous research publications.
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Plastic and Reconstructive Surgery, 1985
Penile curvatures are common. They are caused by tethering inelastic tissues that can be from the skin externally, from the congenital fibrous tissue of hypospadias and epispadias, and from inelastic tunica albuginea as in fractures, trauma, or Peyronie's disease.
C E, Horton +3 more
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Penile curvatures are common. They are caused by tethering inelastic tissues that can be from the skin externally, from the congenital fibrous tissue of hypospadias and epispadias, and from inelastic tunica albuginea as in fractures, trauma, or Peyronie's disease.
C E, Horton +3 more
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Computing Curvature, Mean Curvature and Weighted Mean Curvature
2022 IEEE International Conference on Image Processing (ICIP), 2022openaire +2 more sources
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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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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Riemann Curvature and Ricci Curvature
2012Curvatures 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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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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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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