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Kropina Metrics with Isotropic Scalar Curvature [PDF]

open access: yesAxioms, 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]

open access: yesClassical 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

Scalar curvature in discrete gravity

open access: yesEuropean 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
doaj   +3 more sources

Localized gluing of Riemannian metrics in interpolating their scalar curvature [PDF]

open access: yesarXiv, 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 ...
Delay, Erwann
core   +3 more sources

O(p + 1) x O(p + 1)-Invariant hypersurfaces with zero scalar curvature in euclidean space [PDF]

open access: diamondAnais 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

On Scalar and Ricci Curvatures [PDF]

open access: yesSymmetry, 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
openaire   +5 more sources

On the geometry of the tangent bundle with gradient Sasaki metric [PDF]

open access: yesArab Journal of Mathematical Sciences, 2023
Purpose – Let (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, the authors introduce a new class of natural metrics denoted by gf and called gradient Sasaki metric on the tangent bundle TM. The authors calculate its Levi-Civita
Lakehal Belarbi, Hichem Elhendi
doaj   +1 more source

Estimation of sharp geometric inequality in \(D_{\alpha}\)-homothetically deformed Kenmotsu manifolds

open access: yesCubo, 2023
In this article, we investigate the Kenmotsu manifold when applied to a \(D_{\alpha}\)-homothetic deformation. Then, given a submanifold in a \(D_{\alpha}\)-homothetically deformed Kenmotsu manifold, we derive the generalized Wintgen inequality ...
Mohd Danish Siddiqi   +3 more
doaj   +1 more source

Translation hypersurfaces of semi-Euclidean spaces with constant scalar curvature

open access: yesAIMS Mathematics, 2023
In this paper, we present translation hypersurfaces of semi-Euclidean spaces with zero scalar curvature. In addition, we prove that translation hypersurfaces with constant scalar curvature must have zero scalar curvature in the semi-Euclidean space ...
Derya Sağlam, Cumali Sunar
doaj   +1 more source

On the 2-scalar curvature [PDF]

open access: yesJournal of Differential Geometry, 2010
International ...
Ge, Yuxin   +2 more
openaire   +5 more sources

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