Results 41 to 50 of about 298,518 (247)
Black Holes have Intrinsic Scalar Curvature
Reports in Advances of Physical Sciences, 2023 The scalar curvature R is invariant under isometric symmetries (distance invariance) associated with metric spaces. Gravitational Riemannian manifolds are metric spaces.
P. D. Morley
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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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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
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European Physical Journal C: Particles and Fields, 2023 The observational data of primordial black holes and scalar-induced gravitational waves can constrain the primordial curvature perturbation at small scales. We parameterize the primordial curvature perturbation by a broken power law form and find that it
Zhu Yi, Qin Fei
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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 ...
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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, 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.
Masafumi Okumura, Bang-Yen Chen
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Blowing up and desingularizing constant scalar curvature K\"{a}hler manifolds
, 2005 This paper is concerned with the existence of constant scalar curvature Kaehler metrics on blow ups at finitely many points of compact manifolds which already carry constant scalar curvature Kaehler metrics.
Arezzo, Claudio, Pacard, Frank
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