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Sectional curvature in general relativity
General Relativity and Gravitation, 1987This paper gives a detailed account of the sectional curvature function in general relativity from both the mathematical and the physical viewpoint. Some recent results are rederived by more systematic methods and some new results are obtained. Symmetries of the sectional curvature are also considered, as is the topological structure of the space of ...
Alan D. Rendall, Graham Hall
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Affine hypersurfaces with constant sectional curvature
, 2021M. Antić +3 more
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Negative ξ-sectional Curvature
2002The purpose of this chapter is to introduce some special directions that belong to the contact subbundle of a contact metric manifold with negative sectional curvature for plane sections containing the characteristic vector field ξ or more generally when the operator h admits an eigenvalue greater than 1; these directions were introduced by the author ...
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WEYL-MECHANICAL SYSTEMS ON TANGENT MANIFOLDS OF CONSTANT W-SECTIONAL CURVATURE
, 2013This paper aims to present Weyl–Euler–Lagrange and Weyl–Hamilton equations on $\mathbf{R}_{n}^{2n}$ which is a model of tangent manifolds of Constant W-Sectional Curvature.
Zeki Kasap
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GENERAL RELATIVITY AND SECTIONAL CURVATURE
International Journal of Geometric Methods in Modern Physics, 2006A discussion is given of the sectional curvature function on a four-dimensional Lorentz manifold and, in particular, on the space–time of Einstein's general relativity theory. Its tight relationship to the metric tensor is demonstrated and some of its geometrical and algebraic properties evaluated.
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Sectional Curvature. Spaces of Constant Curvature. Weyl Hypothesis
1997As we have seen, by introducing the notion of curvature tensor K ∇, with any pair of tangent vectors Y, Z ∈ T x M we associated a linear transformation K x (Y, Z) of the tangent space T x M. Let F x be an oriented plane spanned by Y, Z (that is, Y, Z are basis vectors in F x .) Let S F be a surface (in M) generated by geodesics tangent to F, more ...
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Sectional Curvatures and Characteristic Classes
The Annals of Mathematics, 1964We are concerned here with the relationship between the curvature properties of a riemannian manifold X and the global topological and differential invariants of X. An interesting result in this direction is Chern's theorem [6] that if X is compact, orientable, and has constant riemannian sectional curvature, then all Pontrjagin classes of X (with real
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Holomorphic sectional curvature, nefness and Miyaoka–Yau type inequality
Mathematische Zeitschrift, 2018Yashan Zhang
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