Results 61 to 70 of about 298,518 (247)
Remarks on a result of Chen-Cheng
Complex ManifoldsIn their seminal work, Chen and Cheng proved a priori estimates for the constant scalar curvature metrics on compact Kähler manifolds. They also prove C3,α{C}^{3,\alpha }-estimate for the potential of the Kähler metrics under boundedness assumption on ...
Lu Zhiqin, Seyyedali Reza
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Geometric realizations of Kaehler and of para-Kaehler curvature models [PDF]
, 2009 We show that every Kaehler algebraic curvature tensor is geometrically realizable by a Kaehler manifold of constant scalar curvature. We also show that every para-Kaehler algebraic curvature tensor is geometrically realizable by a para-Kaehler manifold of constant scalar ...
arxiv +1 more source
Metrics of constant negative scalar-Weyl curvature [PDF]
arXiv, 2021 Extending Aubin's construction of metrics with constant negative scalar curvature, we prove that every $n$-dimensional closed manifold admits a Riemannian metric with constant negative scalar-Weyl curvature, that is $R+t|W|, t\in\mathbb{R}$. In particular, there are no topological obstructions for metrics with $\varepsilon$-pinched Weyl curvature and ...
arxiv
Scalar curvature and singular metrics [PDF]
Pacific Journal of Mathematics, 2018 47pages, All comments are ...
Yuguang Shi, Luen-Fai Tam
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Certain aspects of regularity in scalar field cosmological dynamics
, 2007 We consider dynamics of the FRW Universe with a scalar field. Using Maupertuis principle we find a curvature of geodesics flow and show that zones of positive curvature exist for all considered types of scalar field potential.
A. Toporensky +19 more
core +1 more source
Semilinear parabolic problems on manifolds and applications to the non-compact Yamabe problem
Electronic Journal of Differential Equations, 2000 We show that the well-known non-compact Yamabe equation (of prescribing constant positive scalar curvature) on a manifold with non-negative Ricci curvature and positive scalar curvature behaving like $c/d(x)^2$ near infinity can not be solved if the ...
Qi S. Zhang
doaj
Massive scalar clouds and black hole spacetimes in Gauss-Bonnet gravity
SciPost Physics CoreWe study static black holes in scalar-Gauss-Bonnet (sGB) gravity with a massive scalar field as an example of higher curvature gravity. The scalar mass introduces an additional scale and leads to a strong suppression of the scalar field beyond its ...
Iris van Gemeren, Tanja Hinderer, Stefan Vandoren
doaj +1 more source
On isotropic Berwald scalar curvature [PDF]
arXiv, 2022 In this short paper, we establish a closer relation between the Berwald scalar curvature and the $S$-curvature. In fact, we prove that a Finsler metric has isotropic Berwald scalar curvature if and only if it has weakly isotropic $S$-curvature. For Finsler metrics of scalar flag curvature and of weakly isotropic $S$-curvature, they have almost ...
arxiv
On the scalar curvature and sectional curvatures of a Kaehler submanifold [PDF]
Proceedings of the American Mathematical Society, 1973 For a Kaehler submanifold of a complex space form, pinching for scalar curvature implies pinching for sectional curvatures. 1 . Statement of result. The scalar curvature is, by definition, the sum of Ricci curvatures with respect to an orthonormal basis of the tangent space, and the Ricci curvature is the sum of sectional curvatures.
Koichi Ogiue, Bang-yen Chen
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Entire Scalar Curvature Flow and Hypersurfaces of Constant Scalar Curvature in Minkowski Space [PDF]
Methods and Applications of Analysis, 2009 We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that the flow converges to a spacelike hypersurface with constant ...
openaire +3 more sources