Results 51 to 60 of about 693,970 (340)
Scalar curvature on compact complex manifolds [PDF]
Transactions of the American Mathematical Society, 2017 In this paper, we prove that, a compact complex manifold $X$ admits a smooth Hermitian metric with positive (resp. negative) scalar curvature if and only if $K_X$ (resp. $K_X^{-1}$) is not pseudo-effective.
Xiaokui Yang
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Two dimensional kinematic surfaces with constant scalar curvature in Lorentz-Minkowski 7-space
Nonlinear Engineering, 2017 In this paper we analyzed the problem of studying locally the scalar curvature S of the two dimensional kinematic surfaces obtained by the homothetic motion of a helix in Lorentz-Minkowski space E17 $\text{E}^7_1$ .
Solouma E. M., Wageeda M. M.
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Convergence of Ricci flows with bounded scalar curvature [PDF]
, 2016 In this paper we prove convergence and compactness results for Ricci flows with bounded scalar curvature and entropy. More specifically, we show that Ricci flows with bounded scalar curvature converge smoothly away from a singular set of codimension ...
R. Bamler
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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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Remarks on critical metrics of the scalar curvature and volume functionals on compact manifolds with boundary [PDF]
Pacific Journal of Mathematics, 2017 We provide a general B\"ochner type formula which enables us to prove some rigidity results for $V$-static spaces. In particular, we show that an $n$-dimensional positive static triple with connected boundary and positive scalar curvature must be ...
H. Baltazar, E. Ribeiro
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Deformation of scalar curvature and volume [PDF]
Mathematische Annalen, 2013 The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points for the volume functional on the space of metrics whose scalar curvature is equal to a given constant.
Corvino, Justin +2 more
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Rigidity of noncompact complete Bach-flat manifolds
, 2010 Let $(M,g)$ be a noncompact complete Bach-flat manifold with positive Yamabe constant. We prove that $(M,g)$ is flat if $(M, g)$ has zero scalar curvature and sufficiently small $L_{2}$ bound of curvature tensor.
Anderson +15 more
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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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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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On the constant scalar curvature Kähler metrics (I)—A priori estimates
Journal of The American Mathematical Society, 2017 In this paper, we derive apriori estimates for constant scalar curvature Kähler metrics on a compact Kähler manifold. We show that higher order derivatives can be estimated in terms of a C 0 C^0 bound for the Kähler potential.
Xiuxiong Chen, Jingrui Cheng
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