共查询到20条相似文献,搜索用时 15 毫秒
1.
Christian Bä r Mattias Dahl 《Proceedings of the American Mathematical Society》2004,132(11):3337-3344
We show that on every compact spin manifold admitting a Riemannian metric of positive scalar curvature Friedrich's eigenvalue estimate for the Dirac operator can be made sharp up to an arbitrarily small given error by choosing the metric suitably.
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We study some of 2n-dimensional conformally flat almost Hermitian manifolds with J-(anti)-invariant Ricci tensor.
Received 13 May 2000; revised 15 February 2001. 相似文献
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Maria Helena Noronha 《Geometriae Dedicata》1993,47(3):255-268
In this paper we study some compact locally conformally flat manifolds with a compatible metric whose scalar curvature is nonnegative, and in particular with nonnegative Ricci curvature. In the last section we study such manifolds of dimension 4 and scalar curvature identically zero. 相似文献
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Non-compact conformally flat manifolds with constant scalar curvature and non-compact Kaehler manifolds with vanishing Bochner curvature are studied and classified.Partially supported by TGRC-KOSEF, 1990. 相似文献
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《Expositiones Mathematicae》2021,39(4):566-582
We discuss the geography problem of closed oriented 4-manifolds that admit a Riemannian metric of positive scalar curvature, and use it to survey mathematical work employed to address Gromov’s observation that manifolds with positive scalar curvature tend to be inessential by focusing on the four-dimensional case. We also point out an strengthening of a result of Carr and its extension to the non-orientable realm. 相似文献
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华义平 《纯粹数学与应用数学》2012,28(3):308-312
M是一个紧致的局部共形平坦黎曼流形,其上定义的Schouten张量是一个Codazzi张量.本文借助这个Codazzi张量引入Cheng和Yau的自伴算子,从而获得了局部共形平坦流形上的一些性质,改进了已有的结论. 相似文献
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Non-spherical hypersurfaces inE
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 the zero and a non-zero constant. 相似文献
10.
R.S. Kraußhar 《Journal of Mathematical Analysis and Applications》2007,325(1):359-376
In this paper we study Clifford and harmonic analysis on some examples of conformal flat manifolds that have a spinor structure, or more generally, at least a pin structure. The examples treated here are manifolds that can be parametrized by U/Γ where U is a subdomain of either Sn or Rn and Γ is a Kleinian group acting discontinuously on U. The examples studied here include RPn and the Hopf manifolds S1×Sn−1. Also some hyperbolic manifolds will be treated. Special kinds of Clifford-analytic automorphic forms associated to the different choices of Γ are used to construct explicit Cauchy kernels, Cauchy integral formulas, Green's kernels and formulas together with Hardy spaces and Plemelj projection operators for Lp spaces of hypersurfaces lying in these manifolds. 相似文献
11.
Satyaki Dutta 《Advances in Mathematics》2010,224(2):525-538
In this paper, we prove that under a lower bound on the Ricci curvature and an assumption on the asymptotic behavior of the scalar curvature, a complete conformally compact manifold whose conformal boundary is the round sphere has to be the hyperbolic space. It generalizes similar previous results where stronger conditions on the Ricci curvature or restrictions on dimension are imposed. 相似文献
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Zhang Zonglao 《Proceedings Mathematical Sciences》2005,115(3):309-318
This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature.
We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some nonexistence results
for complete solutions of scalar curvature equation. 相似文献
14.
Jaeman Kim 《Czechoslovak Mathematical Journal》2006,56(1):267-271
On a 4-dimensional anti-Kähler manifold, its zero scalar curvature implies that its Weyl curvature vanishes and vice versa. In particular any 4-dimensional anti-Kähler manifold with zero scalar curvature is flat. 相似文献
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We prove that a Finsler manifold with vanishing Berwald scalar curvature has zero E-curvature. As a consequence, Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds. For (α,β)-metrics on manifold of dimension greater than 2, if the mean Landsberg curvature and the Berwald scalar curvature both vanish, then the Berwald curvature also vanishes. 相似文献
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For any 3-manifold M3 and any nonnegative integer g, we give here examples of metrics on M each of which has a sequence of embedded minimal surfaces of genus g and without Morse index bounds. On any spherical space form we construct such a metric with positive scalar curvature. More generally, we construct such a metric with Scal>0 (and such surfaces) on any 3-manifold which carries a metric with Scal>0. 相似文献
17.
Bang-Yen Chen Franki Dillen Leopold Verstraelen Luc Vrancken 《Proceedings of the American Mathematical Society》2000,128(2):589-598
In a recent paper the first author introduced two sequences of Riemannian invariants on a Riemannian manifold , denoted respectively by and , which trivially satisfy . In this article, we completely determine the Riemannian manifolds satisfying the condition . By applying the notions of these -invariants, we establish new characterizations of Einstein and conformally flat spaces; thus generalizing two well-known results of Singer-Thorpe and of Kulkarni.
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M. Brozos-Vzquez P. Gilkey H. Kang S. Nik
evi G. Weingart 《Differential Geometry and its Applications》2009,27(6):696-701
We show any pseudo-Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyper-pseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with constant scalar and -scalar curvature. 相似文献
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A Finsler metric on a manifold M with its flag curvature K is said to be almost isotropic flag curvature if K =3c + σ where σ and c are scalar functions on M.In this paper,we establish the intrinsic re... 相似文献
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Guangyue Huang 《Annals of Global Analysis and Geometry》2018,54(2):257-272
For the Bach-flat closed manifold with positive scalar curvature, we prove a rigidity theorem involving the Weyl curvature and the traceless Ricci curvature. Moreover, we provide a similar rigidity result with respect to the \(L^{\frac{n}{2}}\)-norm of the Weyl curvature, the traceless Ricci curvature, and the Yamabe invariant. In particular, we also obtain rigidity results in terms of the Euler–Poincaré characteristic. 相似文献