Results 21 to 30 of about 193,587 (326)
Scalar Curvature and Q-Curvature of Random Metrics [PDF]
The Journal of Geometric Analysis, 2010 We study Gauss curvature for random Riemannian metrics on a compact surface, lying in a fixed conformal class; our questions are motivated by comparison geometry. Next, analogous questions are considered for the scalar curvature in dimension $n>2$, and for the $Q$-curvature of random Riemannian metrics.
Canzani, Yaiza +2 more
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On Gromov’s scalar curvature conjecture [PDF]
Proceedings of the American Mathematical Society, 2009 We prove the Gromov conjecture on the macroscopic dimension of the universal covering of a closed spin manifold with a positive scalar curvature under the following assumptions on the fundamental group.0.10.1.Theorem.Suppose that a discrete groupπ\pihas the following properties:11. The Strong Novikov Conjecture holds forπ\pi.22.
Bolotov, Dmitry, Dranishnikov, Alexander
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Scalar curvature, inequality and submanifold [PDF]
Proceedings of the American Mathematical Society, 1973 Using an inequality relation between scalar curvature and length of second fundamental form, we may conclude that a submanifold must have nonnegative (or positive) sectional curvatures. An application to compact submanifolds in obtained.
Chen, Bang-Yen, Okumura, Masafumi
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TOTAL SCALAR CURVATURE AND HARMONIC CURVATURE
Taiwanese Journal of Mathematics, 2014 On a compact n-dimensional manifold, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will be Einstein. This conjecture was proposed in 1984 by Besse, but has yet to be proved.
Yun, Gabjin +2 more
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Kretschmann Invariant and Relations Between Spacetime Singularities Entropy and Information [PDF]
, 2014 Curvature invariants are scalar quantities constructed from tensors that represent curvature. One of the most basic polynomial curvature invariants in general relativity is the Kretschmann scalar.
Gkigkitzis, Ioannis +2 more
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Scalar curvature of Lie groups [PDF]
Proceedings of the American Mathematical Society, 1981 In this paper, we prove the following theorem: If G G is a connected Lie group, then G G admits left invariant metric of positive scalar curvature if and only if the universal covering space G ~ \tilde G of G G is not homeomorphic to the ...
Lai, Heng-Lung, Lue, Huei-Shyong
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Renormalizable Gravitational Action That Reduces to General Relativity on the Mass-Shell
Galaxies, 2018 We derive the equation that relates gravity to quantum mechanics: R|mass-shell=8πGc4LSM, where R is the scalar curvature, G is the gravitational constant, c is the speed of light and LSM is the Standard Model Lagrangian, or its future replacement ...
Peter D. Morley
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Geometric Inequalities for a Submanifold Equipped with Distributions
Mathematics, 2022 The article introduces invariants of a Riemannian manifold related to the mutual curvature of several pairwise orthogonal subspaces of a tangent bundle. In the case of one-dimensional subspaces, this curvature is equal to half the scalar curvature of the
Vladimir Rovenski
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Non-negative versus positive scalar curvature
, 2020 We show that results about spaces or moduli spaces of positive scalar curvature metrics proved using index theory can typically be extended to non-negative scalar curvature metrics.
Schick, Thomas, Wraith, David J.
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Curvature operators and scalar curvature invariants [PDF]
Classical and Quantum Gravity, 2010 We continue the study of the question of when a pseudo-Riemannain manifold can be locally characterised by its scalar polynomial curvature invariants (constructed from the Riemann tensor and its covariant derivatives). We make further use of alignment theory and the bivector form of the Weyl operator in higher dimensions, and introduce the important ...
Hervik, Sigbjørn, Coley, Alan
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