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Conjectures on Convergence and Scalar Curvature
, 2021 Here we survey the compactness and geometric stability conjectures formulated by the participants at the 2018 IAS Emerging Topics Workshop on {\em Scalar Curvature and Convergence}.
Convergence +2 more
core
Scalar curvature and projective compactness
Journal of Geometry and Physics, 2015 Final version to be published in J. Geom. Phys. Includes minor typo corrections and a new summarising corollary.
Andreas Cap, A. Rod Gover
openaire +4 more sources
Intrinsic problems of the gravitational baryogenesis
Physics Letters B, 2017 Modification of gravity due to the curvature dependent term in the gravitational baryogenesis scenario is considered. It is shown that this term leads to the fourth order differential equation of motion for the curvature scalar instead of the algebraic ...
E.V. Arbuzova, A.D. Dolgov
doaj +1 more source
Critical metrics of the $L^2$-norm of the scalar curvature
, 2013 In this paper we investigate complete critical metrics of the $L^{2}$-norm of the scalar curvature. We prove that any complete critical metric with positive scalar curvature has constant scalar curvature and we characterize critical metrics with ...
Catino, Giovanni
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Curvature-Dimension Condition Meets Gromov's $n$-Volumic Scalar Curvature [PDF]
SIGMA 17 (2021), 013, 20 pages, 2020 We study the properties of the $n$-volumic scalar curvature in this note. Lott-Sturm-Villani's curvature-dimension condition ${\rm CD}(\kappa,n)$ was showed to imply Gromov's $n$-volumic scalar curvature $\geq n\kappa$ under an additional $n$-dimensional condition and we show the stability of $n$-volumic scalar curvature $\geq \kappa$ with respect to ...
arxiv +1 more source
On the scalar curvature of complex surfaces [PDF]
Geometric and Functional Analysis, 1995 10 pages, LaTeX, with optional \Bbb font replaceable by ...
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AIMS MathematicsThe Ricci curvature in Finsler geometry naturally generalizes the Ricci curvature in Riemannian geometry. In this paper, we study the -th root metric with weakly isotropic scalar curvature and obtain that its scalar curvature must vanish.
Xiaoling Zhang, Cuiling Ma, Lili Zhao
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Scalar Curvature via Local Extent
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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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 ...
Huei Shyong Lue, Hêng Lung Lai
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Derivative couplings in gravitational production in the early universe
Journal of High Energy Physics, 2020 Gravitational particle production in the early universe is due to the coupling of matter fields to curvature. This coupling may include derivative terms that modify the kinetic term.
Daniel E. Borrajo Gutiérrez +3 more
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