共查询到20条相似文献,搜索用时 31 毫秒
1.
Jaeman Kim 《Geometriae Dedicata》2000,80(1-3):281-287
We will prove that every Einstein–Thorpe metric on T
8 must be flat and that on compact oriented hyperbolic manifolds of dimension 8, every Einstein–Thorpe metric is a hyperbolic metric up to rescalings and diffeomorphisms. 相似文献
2.
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
3.
本文研究了Berwald流形之间的射影对应.利用Berwald流形上Weyl射影曲率张量的射影不变性,证明了当n>2时,与射影平坦的Berwald流形射影对应的黎曼流形M~n是常曲率流形,从而推广了Beltrami定理. 相似文献
4.
The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. ... 相似文献
5.
S. Azimpour M. Chaichi M. Toomanian 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2007,42(5):270-277
A 4-dimensional Walker metric on a semi Riemanian manifold M, for the canonical metric with c = 0, have been investigated by M. Chaichi, E. García—Río and Y. Matsushita. The paper generalizes these notions to the case of constant c ≠ 0. Specially the form of defining functions of this metric in locally conformally flat 4-dimensional Walker manifolds is found. 相似文献
6.
§1. IntroductionLetMbeann-dimensionalconformallyflatmanifoldwithconstantscalarcurvatureρ(n≥3).WhentheRiccicurvatureSofMisofboundedbelowandySy2<ρ2/(n-1),Gold-bergprovedthatMisofconstantcurvature[1].WhenMisacompactmanifoldwithpositiveRiccicurvature,WuB… 相似文献
7.
Projectively flat Matsumoto metric and its approximation 总被引:1,自引:0,他引:1
李本伶 《数学物理学报(B辑英文版)》2007,27(4):781-789
In this article, the author studies the projectively flat Matsumoto metric F=α2/(α - β), where α=√aijyiyj is a Riemannian metric and β=biyi is a 1-form. They conclude that α is locally projectively flat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric. 相似文献
8.
We will prove that normal complex contact metric manifolds that are Bochner flat must have constant holomorphic sectional curvature 4 and be Kähler. If they are also complete and simply connected, they must be isometric to the odd-dimensional complex projective space \({{\mathbb{C}P^{2n+1}}}\)(4) with the Fubini-Study metric. On the other hand, it is not possible for normal complex contact metric manifolds to be conformally flat. 相似文献
9.
Benling Li 《Differential Geometry and its Applications》2013,31(6):718-724
In this paper, we study the locally dually flat Finsler metrics which arise from information geometry. An equivalent condition of locally dually flat Finsler metrics is given. We find a new method to construct locally dually flat Finsler metrics by using a projectively flat Finsler metric under the condition that the projective factor is also a Finsler metric. Finally, we find that many known Finsler metrics are locally dually flat Finsler metrics determined by some projectively flat Finsler metrics. 相似文献
10.
任新安 《数学物理学报(B辑英文版)》2009,29(2):447-455
In [6], a global solution of Yang-Mills equation on de-Sitter spacetime with conformal fiat metric was given by Prof. Lu. In this article, Yang-Mills equation on ndimensional de-Sitter space with Beltrami-Hua-Lu metric is discussed and a global solution is obtained. 相似文献
11.
Gianluca Bande David E. Blair Amine Hadjar 《Mediterranean Journal of Mathematics》2013,10(2):989-1009
We consider manifolds endowed with metric contact pairs for which the two characteristic foliations are orthogonal. We give some properties of the curvature tensor and in particular a formula for the Ricci curvature in the direction of the sum of the two Reeb vector fields. This shows that metrics associated to normal contact pairs cannot be flat. Therefore flat non-Kähler Vaisman manifolds do not exist. Furthermore we give a local classification of metric contact pair manifolds whose curvature vanishes on the vertical subbundle. As a corollary we have that flat associated metrics can only exist if the leaves of the characteristic foliations are at most three-dimensional. 相似文献
12.
Using the heat kernel, we derive first a local Gauss–Bonnet–Chern theorem for manifolds with a non-product metric near the
boundary. Then we establish an anomaly formula for Ray–Singer metrics defined by a Hermitian metric on a flat vector bundle
over a Riemannian manifold with boundary, not assuming that the Hermitian metric on the flat vector bundle is flat nor that
the Riemannian metric has product structure near the boundary.
Received: January 2004; Revision: February 2005; Accepted: September 2005 相似文献
13.
Yan Li 《Frontiers of Mathematics in China》2017,12(3):597-606
In this note, we investigate the behavior of a smooth flat family of n-dimensional conic negative Kähler-Einstein manifolds. By H. Guenancia’s argument, a cusp negative Kähler-Einstein metric is the limit of conic negative Kähler-Einstein metric when the cone angle tends to 0. Furthermore, it establishes the behavior of a smooth flat family of n-dimensional cusp negative Kähler-Einstein manifolds. 相似文献
14.
J. M. Kim 《Acta Mathematica Hungarica》2003,100(4):265-270
We show that in dimension 8, a semiflat metric is flat and that in dimension (8k+4) higher than 8, a semiflat metric does not necessarily imply flat.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
A. V. Chakmazyan 《Mathematical Notes》1977,22(5):853-860
The concept of a p-dimensional parallel subbundle of the normal bundle of a submanifold Vm of n-dimensional protective space Pn normalized in the sense of Norden [1] is introduced. The local structure of such manifolds is studied. The structure is also investigated of submanifolds Vm which have normal subbundles with a flat projective connection. Their structure is closely related with the structure of tangentially degenerate submanifolds [2, 3] and submanifolds admitting a dual normalization [4].Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 649–662, November, 1977.I express my sincere gratitude to M. A. Akivis and Yu. G. Lyumista for valuable comments which they made in duscussing the results of this paper. 相似文献
16.
In this paper, we derive the Cheeger–Müller/Bismut–Zhang theorem for manifolds with boundary and the gluing formula for the analytic torsion of flat vector bundles in full generality, i.e., we do not assume that the Hermitian metric on the flat vector bundle is flat nor that the Riemannian metric has product structure near the boundary. 相似文献
17.
Amalendu Ghosh 《Results in Mathematics》2014,65(1-2):81-94
We show that if a compact K-contact metric is a gradient Ricci almost soliton, then it is isometric to a unit sphere S 2n+1. Next, we prove that if the metric of a non-Sasakian (κ, μ)-contact metric is a gradient Ricci almost soliton, then in dimension 3 it is flat and in higher dimensions it is locally isometric to E n+1 × S n (4). Finally, a couple of results on contact metric manifolds whose metric is a Ricci almost soliton and the potential vector field is point wise collinear with the Reeb vector field of the contact metric structure were obtained. 相似文献
18.
Graham Hall 《Central European Journal of Mathematics》2012,10(5):1763-1770
This paper discusses the connection between projective relatedness and conformal flatness for 4-dimensional manifolds admitting
a metric of signature (+,+,+,+) or (+,+,+,−). It is shown that if one of the manifolds is conformally flat and not of the
most general holonomy type for that signature then, in general, the connections of the manifolds involved are the same and
the second manifold is also conformally flat. Counterexamples are provided which place limitations on the potential strengthening
of the results. 相似文献
19.
Ramesh Sharma 《Journal of Geometry》1995,53(1-2):179-190
Some results on Ricci-symmetric contact metric manifolds are obtained. Second order parallel tensors and vector fields keeping curvature tensor invariant are characterized on a class of contact manifolds. Conformally flat contact manifolds are studied assuming certain curvature conditions. Finally some results onk-nullity distribution of contact manifolds are obtained. 相似文献
20.
Mancho Manev 《Journal of Geometry》2012,103(3):519-530
Almost hypercomplex manifolds with Hermitian and Norden metrics and more specially the corresponding quaternionic Kähler manifolds are considered. Some necessary and sufficient conditions for the investigated manifolds to be isotropic hyper-Kählerian and flat are found. It is proved that the quaternionic Kähler manifolds with the considered metric structure are Einstein for dimension at least 8. The class of the non-hyper-Kähler quaternionic Kähler manifolds of the considered type is determined. 相似文献