Results 11 to 20 of about 192,579 (307)
Scalar Curvature via Local Extent [PDF]
Analysis and Geometry in Metric Spaces, 2018 We give a metric characterization of the scalar curvature of a smooth Riemannian manifold, analyzing the maximal distance between (n + 1) points in infinitesimally small neighborhoods of a point.
Veronelli Giona
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Kinetic scalar curvature extended f(R) gravity
Nuclear Physics B, 2018 In this work we study a modified version of vacuum f(R) gravity with a kinetic term which consists of the first derivatives of the Ricci scalar. We develop the general formalism of this kinetic Ricci modified f(R) gravity and we emphasize on cosmological
S.V. Chervon +4 more
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On scalar curvature lower bounds and scalar curvature measure [PDF]
Advances in Mathematics, 2021 We relate the (non)existence of lower scalar curvature bounds to the existence of certain distance-decreasing maps. We also give a sufficient condition for the existence of a limiting scalar curvature measure in the backward limit of a Ricci flow solution.
John Lott
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On Scalar and Ricci Curvatures [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 The purpose of this report is to acknowledge the influence of M. Gromov's vision of geometry on our own works. It is two-fold: in the first part we aim at describing some results, in dimension 3, around the question: which open 3-manifolds carry a complete Riemannian metric of positive or non negative scalar curvature?
Besson, Gérard, Gallot, Sylvestre
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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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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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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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