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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
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On scalar curvature lower bounds and scalar curvature measure [PDF]
Advances in Mathematics, 2022 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.
Lott, John
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Deformation of the Weighted Scalar Curvature
Symmetry, Integrability and Geometry: Methods and Applications, 2023 Inspired by the work of Fischer-Marsden [Duke Math. J. 42 (1975), 519-547], we study in this paper the deformation of the weighted scalar curvature. By studying the kernel of the formal $L_\phi^2$-adjoint for the linearization of the weighted scalar curvature, we prove several geometric results.
Ho, Pak Tung, Shin, Jinwoo
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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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Perspectives in Scalar Curvature [PDF]
, 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}.
Mikhail L Gromov, H Blaine Lawson, Jr.
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Boundary Conditions for Scalar Curvature [PDF]
, 2023 Minor typos fixed.
Baer, Christian, Hanke, Bernhard
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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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On the geometry of the tangent bundle with gradient Sasaki metric [PDF]
Arab 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
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Cubo, 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
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Foliated Positive Scalar Curvature [PDF]
, 2021 In this thesis we study different questions on scalar curvatures. The first part is devoted to obstructions against existence of a (Riemannian) metric with positive scalar curvature on a closed manifold.
Deng, Jialong
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