共查询到20条相似文献,搜索用时 15 毫秒
1.
Jaeman Kim 《Annals of Global Analysis and Geometry》2009,35(4):339-343
We prove that every irreducible Kähler manifold with harmonic Bochner curvature tensor and constant scalar curvature is Kähler–Einstein and that every irreducible compact Kähler manifold with harmonic Bochner curvature tensor and negative semi-definite Ricci tensor is Kähler–Einstein. 相似文献
2.
In the framework of studying the integrability of almost Kähler manifolds, we prove that a four-dimensional almost Kähler Einstein and -Einstein manifold is a Kähler manifold. Further, we estimate the *-scalar curvature of a four-dimensional compact almost Kähler Einstein and weakly *-Einstein manifold with negative scalar curvature. 相似文献
3.
This paper is concerned with the existence of constant scalar curvature Kähler metrics on blow-ups at finitely many points of compact manifolds which already carry constant scalar curvature Kähler metrics. We also consider the desingularization of isolated quotient singularities of compact orbifolds which carry constant scalar curvature Kähler metrics. 相似文献
4.
We consider compact Kähler manifolds with their Kähler Ricci tensor satisfying F(Ric) = constant. Under the nonnegative bisectional curvature assumption and certain conditions on F, we prove that such metrics are in fact Kähler–Einstein. 相似文献
5.
In the present article, we extend the integral formula on a compact almost Kähler manifold with positive-definite metric to the one on a compact indefinite almost Kähler manifold and give its applications for some special indefinite almost Kähler Einstein manifolds taking the related problems to the indefinite analogy of Goldberg conjecture into consideration. 相似文献
6.
Jaeman Kim 《Periodica Mathematica Hungarica》2012,64(1):25-28
The Riemannian version of the Goldberg-Sachs theorem says that a compact Einstein Hermitian surface is locally conformal Kähler. In contrast to the compact case, we show that there exists an Einstein Hermitian surface which is not locally conformal Kähler. On the other hand, it is known that on a compact Hermitian surface M 4, the zero scalar curvature defect implies that M 4 is Kähler. Contrary to the compact case, we show that there exists a non-Kähler Hermitian surface with zero scalar curvature defect. 相似文献
7.
Dezhong Chen 《Annals of Global Analysis and Geometry》2011,40(3):339-377
We construct Einstein metrics of non-positive scalar curvature on certain solid torus bundles over a Fano Kähler–Einstein manifold. We show, among other things, that the negative Einstein metrics are conformally compact, and the Ricci-flat metrics have slower-than-Euclidean volume growth and quadratic curvature decay. Also we construct positive Einstein metrics on certain 3-sphere bundles over a Fano Kähler–Einstein manifold. We classify the homeomorphism and diffeomorphism types of the total spaces when the base is the complex projective plane. 相似文献
8.
Martin Bridgeman Richard Canary François Labourie Andres Sambarino 《Geometriae Dedicata》2018,195(1):57-78
On a Kähler manifold there is a clear connection between the complex geometry and underlying Riemannian geometry. In some ways, this can be used to characterize the Kähler condition. While such a link is not so obvious in the non-Kähler setting, one can seek to understand extensions of these characterizations to general Hermitian manifolds. This idea has been the subject of much study from the cohomological side, however, the focus here is to address such a question from the perspective of curvature relationships. In particular, on compact manifolds the Kähler condition is characterized by the relationship that the Chern scalar curvature is equal to half the Riemannian scalar curvature. What we study here is the existence, or lack thereof, of non-Kähler Hermitian metrics for which a more general proportionality relationship between these scalar curvatures holds. 相似文献
9.
For a Kähler metric, the Riemannian scalar curvature is equal to twice the Chern scalar curvature. The question we address here is whether this equivalence can hold for a non-Kähler Hermitian metric. For such metrics, if they exist, the Chern scalar curvature would have the same geometric meaning as the Riemannian scalar curvature. Recently, Liu–Yang showed that if this equivalence of scalar curvatures holds even in average over a compact Hermitian manifold, then the metric must in fact be Kähler. However, we prove that a certain class of non-compact complex manifolds do admit Hermitian metrics for which this equivalence holds. Subsequently, the question of to what extent the behavior of said metrics can be dictated is addressed and a classification theorem is proved. 相似文献
10.
J. Ross 《Inventiones Mathematicae》2006,165(1):153-162
We give examples of smooth manifolds with negative first Chern class which are slope unstable with respect to certain polarisations, and so have Kähler classes that do not admit any constant scalar curvature Kähler metrics. These manifolds also have unstable Hilbert and Chow points. We compare this to the work of Song-Weinkove on the J-flow. 相似文献
11.
Motivated by a previous work by Zheng and the second-named author, we study pinching constants of compact Kähler manifolds with positive holomorphic sectional curvature. In particular, we prove a gap theorem on Kähler manifolds with almost-one-half pinched holomophic sectional curvature. The proof is motivated by the work of Petersen and Tao on Riemannian manifolds with almost-quarter-pinched sectional curvature. 相似文献
12.
We show that if a Fano manifold M is K-stable with respect to special degenerations equivariant under a compact group of automorphisms, then M admits a Kähler–Einstein metric. This is a strengthening of the solution of the Yau–Tian–Donaldson conjecture for Fano manifolds by Chen–Donaldson–Sun (Int Math Res Not (8):2119–2125, 2014), and can be used to obtain new examples of Kähler–Einstein manifolds. We also give analogous results for twisted Kähler–Einstein metrics and Kahler–Ricci solitons. 相似文献
13.
K.-D. Kirchberg 《Annals of Global Analysis and Geometry》2010,38(3):273-284
In the case of a Kähler–Einstein manifold of positive scalar curvature and even complex dimension, an improved lower bound for the first eigenvalue of the Dirac operator is given. It is shown by a general construction that there are manifolds for which this new lower bound itself is the first eigenvalue. 相似文献
14.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》2001,332(3):245-248
In this Note, we announce the result that if M is a Kähler–Einstein manifold with positive scalar curvature, if the initial metric has nonnegative bisectional curvature, and the curvature is positive somewhere, then the Kähler–Ricci flow converges to a Kähler–Einstein metric with constant bisectional curvature. 相似文献
15.
Zakarias Sjöström Dyrefelt 《Journal of Geometric Analysis》2018,28(4):2927-2960
We prove that constant scalar curvature Kähler (cscK) manifolds with transcendental cohomology class are K-semistable, naturally generalising the situation for polarised manifolds. Relying on a recent result by R. Berman, T. Darvas and C. Lu regarding properness of the K-energy, it moreover follows that cscK manifolds with discrete automorphism group are uniformly K-stable. As a main step of the proof we establish, in the general Kähler setting, a formula relating the (generalised) Donaldson–Futaki invariant to the asymptotic slope of the K-energy along weak geodesic rays. 相似文献
16.
L. C. de Andrés M. Fernández S. Ivanov J. A. Santisteban L. Ugarte D. Vassilev 《Annali di Matematica Pura ed Applicata》2014,193(1):261-290
We construct left-invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic contact manifolds. We prove that the product of the real line with a seven-dimensional manifold, equipped with a certain qc structure, has a quaternionic Kähler metric as well as a metric with holonomy contained in Spin(7). As a consequence, we determine explicit quaternionic Kähler metrics and Spin(7)-holonomy metrics, which seem to be new. Moreover, we give explicit non-compact eight dimensional almost quaternion hermitian manifolds that are not quaternionic Kähler with either a closed fundamental four form or fundamental two forms defining a differential ideal. 相似文献
17.
Lars Schäfer 《Monatshefte für Mathematik》2011,163(3):339-371
Firstly we give a condition to split off the Kähler factor from a nearly pseudo-Kähler manifold and apply this to get a structure result in dimension 8. Secondly we extend the construction of nearly Kähler manifolds from twistor spaces to negatively curved quaternionic Kähler manifolds and para-quaternionic Kähler manifolds. The class of nearly pseudo-Kähler manifolds obtained from this construction is characterized by a holonomic condition. The combination of these results enables us to give a classification result in (real) dimension 10. Moreover, we show that a strict nearly pseudo-Kähler six-manifold is Einstein. 相似文献
18.
Weiyong He 《Journal of Geometric Analysis》2013,23(4):1876-1931
We show that Perelman’s ${\mathcal{W}}$ functional on Kähler manifolds has a natural counterpart on Sasaki manifolds. We prove, using this functional, that Perelman’s results on Kähler–Ricci flow (the first Chern class is positive) can be generalized to Sasaki–Ricci flow, including the uniform bound on the diameter and the scalar curvature along the flow. We also show that positivity of transverse bisectional curvature is preserved along Sasaki–Ricci flow, using Bando and Mok’s methods and results in Kähler–Ricci flow. In particular, we show that the Sasaki–Ricci flow converges to a Sasaki–Ricci soliton when the initial metric has nonnegative transverse bisectional curvature. 相似文献
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20.
ChengJie Yu 《中国科学 数学(英文版)》2017,60(2):285-300
We systematically derive the Bianchi identities for the canonical connection on an almost Hermitian manifold.Moreover,we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection.As applications of the curvature identities,we obtain some results about the integrability of quasi K¨ahler manifolds and nearly K¨ahler manifolds. 相似文献