Results 1 to 10 of about 79,734 (334)
Constant scalar curvature metrics on connected sums [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 The Yamabe problem (proved in 1984) guarantees the existence of a metric of constant scalar curvature in each conformal class of Riemannian metrics on a compact manifold of dimension n ≥ 3, which minimizes the total scalar curvature on this conformal class. Let (M′, g′) and (M″, g″) be compact Riemannian n‐manifolds. We form their connected sumM′#M″ by
Dominic Joyce
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On nonlocal gravity with constant scalar curvature
Publications de l'Institut Mathematique, 2018 A class of nonlocal gravity models, where nonlocal term contains an analytic function of the d’Alembert operator , is considered. For simplicity, these models are considered without matter sector. Related equations of motion for gravitational field gμν(x)
I. Dimitrijevic +3 more
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Geodesic mappings of quasi-Einstein spaces with a constant scalar curvature
Математичні Студії, 2020 In this paper we study a special type of pseudo-Riemannian spaces - quasi-Einstein spaces of constant scalar curvature. These spaces are generalizations of known Einstein spaces.
V. A. Kiosak, G. V. Kovalova
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Universality and Constant Scalar Curvature Invariants [PDF]
ISRN Geometry, 2011 A classical solution is called universal if the quantum correction is a multiple of the metric. Therefore, universal solutions play an important role in the quantum theory. We show that in a spacetime which is universal all scalar curvature invariants are constant (i.e., the spacetime is CSI).
Coley, A. A., Hervik, S.
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Hypersurfaces with constant scalar curvature and constant mean curvature
Annals of Global Analysis and Geometry, 1995 According to the authors' abstract, ``non-spherical hypersurfaces in \(E^ 4\) with non-zero constant mean curvature and constant scalar curvature are the only hypersurfaces possessing the following property: Its position vector can be written as a sum of two non-constant maps, which are eigenmaps of the Laplacian operator with corresponding eigenvalues
Hasanis, T., Vlachos, T.
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On coupled constant scalar curvature Kähler metrics [PDF]
Journal of Symplectic Geometry, 2019 We provide a moment map interpretation for the coupled K\"ahler-Einstein equations introduced by Hultgren and Witt Nystr\"om, and in the process introduce a more general system of equations, which we call coupled cscK equations.
V. Datar, V. Pingali
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Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds [PDF]
Communications in Contemporary Mathematics, 2016 We study the problem of deforming a Riemannian metric to a conformal one with nonzero constant scalar curvature and nonzero constant boundary mean curvature on a compact manifold of dimension [Formula: see text].
Xuezhang Chen, Liming Sun
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Hypersurfaces with constant scalar curvature
Mathematische Annalen, 1977 Let M be a complete two-dimensional surface immersed into the three-dimensional Euclidean space. Then a classical theorem of Hilbert says that when the curvature of M is a non-zero constant, M must be the sphere. On the other hand, when the curvature of M is zero, a theorem of Har tman-Nirenberg [4] says that M must be a plane or a cylinder.
Shiu-Yuen Cheng, Shing-Tung Yau
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On the constant scalar curvature Kähler metrics (II)—Existence results
Journal of the American Mathematical Society, 2020 In this paper, we apply our previous estimates in Chen and Cheng [On the constant scalar curvature Kähler metrics (I): a priori estimates, Preprint] to study the existence of cscK metrics on compact Kähler manifolds. First we prove that the properness of
Xiuxiong Chen, Jingrui Cheng
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Biharmonic hypersurfaces with constant scalar curvature in space forms [PDF]
, 2016 Let $M^n$ be a biharmonic hypersurface with constant scalar curvature in a space form $\mathbb M^{n+1}(c)$. We show that $M^n$ has constant mean curvature if $c>0$ and $M^n$ is minimal if $c\leq0$, provided that the number of distinct principal ...
Yu Fu, Minhao Hong
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