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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.
J. Lott
semanticscholar +3 more sources
Kropina Metrics with Isotropic Scalar Curvature [PDF]
Axioms, 2023 In this paper, we study Kropina metrics with isotropic scalar curvature. First, we obtain the expressions of Ricci curvature tensor and scalar curvature. Then, we characterize the Kropina metrics with isotropic scalar curvature on by tensor analysis.
Liulin Liu, Xiaoling Zhang, Lili Zhao
doaj +2 more sources
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).
Alan Coley +15 more
core +6 more sources
Boundary Conditions for Scalar Curvature [PDF]
, 2020 Based on the Atiyah-Patodi-Singer index formula, we construct an obstruction to positive scalar curvature metrics with mean convex boundaries on spin manifolds of infinite K-area. We also characterize the extremal case. Next we show a general deformation
Christian Baer, B. Hanke
semanticscholar +4 more sources
Scalar curvature in discrete gravity
European Physical Journal C: Particles and Fields, 2022 We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings.
Ali H. Chamseddine +2 more
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Mean Curvature in the Light of Scalar Curvature [PDF]
Annales de l'Institut Fourier, 2018 We formulate several conjectures on mean convex domains in the Euclidean spaces, as well as in more general spaces with lower bonds on their scalar curvatures, and prove a few theorems motivating these conjectures.
M. Gromov
semanticscholar +5 more sources
Circle actions and scalar curvature [PDF]
Transactions of the American Mathematical Society, 2015 We construct metrics of positive scalar curvature on manifolds with circle actions. One of our main results is that there exist $S^1$-invariant metrics of positive scalar curvature on every $S^1$-manifold which has a fixed point component of codimension ...
Wiemeler, Michael
core +5 more sources
Metric Inequalities with Scalar Curvature [PDF]
Geometric and Functional Analysis, 2017 We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces with positive sectional curvature.
M. Gromov
semanticscholar +4 more sources
Localized gluing of Riemannian metrics in interpolating their scalar curvature [PDF]
arXiv, 2010 We show that two smooth nearby Riemannian metrics can be glued interpolating their scalar curvature. The resulting smooth metric is the same as the starting ones outside the gluing region and has scalar curvature interpolating between the original ones. One can then glue metrics while maintaining inequalities satisfied by the scalar curvature.
Delay, Erwann
arxiv +4 more sources
O(p + 1) x O(p + 1)-Invariant hypersurfaces with zero scalar curvature in euclidean space [PDF]
Anais da Academia Brasileira de Ciências, 2000 We use equivariant geometry methods to study and classify zero scalar curvature O(p + 1) x O(p + 1)-invariant hypersurfaces in R2p+2 with p > 1.
JOCELINO SATO
doaj +2 more sources