共查询到20条相似文献,搜索用时 750 毫秒
1.
Fortuné Massamba 《Mediterranean Journal of Mathematics》2013,10(2):1079-1099
Null hypersurfaces have metrics with vanishing determinants and this degeneracy of these metrics leads to several difficulties. In this paper, null hypersurfaces of indefinite Kenmotsu space forms, tangent to the structure vector field, are studied with specific attention to locally symmetric, semi-symmetric and Ricci semi-symmetric null hypersurfaces. We show that locally symmetric and semi-symmetric null hypersurfaces are totally geodesic and parallel. These also hold for Ricci semi-symmetric null hypersurfaces, under a certain condition. We prove that, in null Einstein hypersurfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the local symmetry, semisymmetry and Ricci semi-symmetry notions are equivalent. For totally contact umbilical null hypersurfaces, we show that there are η-“Weyl” connections adapted to the induced structure on the null hypersurface. 相似文献
2.
G. Calvaruso 《Acta Mathematica Hungarica》2008,121(1-2):157-170
Because of the different possible forms (Segre types) of the Ricci operator, semi-symmetry assumption for the curvature of a Lorentzian manifold turns out to have very different consequences with respect to the Riemannian case. In fact, a semi-symmetric homogeneous Riemannian manifold is necessarily symmetric, while we find some three-dimensional homogeneous Lorentzian manifolds which are semi-symmetric but not symmetric. The complete classification of three-dimensional semi-symmetric homogeneous Lorentzian manifolds is obtained. 相似文献
3.
The purpose of the present paper is to prove that a Kaehler hypersurface with the cyclic Ricci semi-symmetric tensor is locally symmetric. 相似文献
4.
We characterize semi-symmetric Lorentzian three-manifolds (M,g
f
) admitting a parallel degenerate line field, through a condition on the defining function f. The admissible Segre types of the Ricci operator of (M,g
f
) are also completely described, and semi-symmetric curvature homogeneous examples are presented in the possible different
cases. 相似文献
5.
M. Faghfouri A. Haji Badali E. Pourreza 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(4):214-220
In this paper we determine a Blaschke structure for affine immersion of Euclidian and Hyperbolic type for plane equi-affine curve. In particular, we consider this structure in the case where the Ricci tensor of affine immersion is constant and give a necessary and sufficient condition for Ricci tensor to be constant. 相似文献
6.
本文研究了容有半对称度量联络的广义复空间中的子流形上的Chen-Ricci不等式.利用代数技巧,建立了子流形上的Chen-Ricci不等式.这些不等式给出了子流形的外在几何量-关于半对称联络的平均曲率与内在几何量-Ricci曲率及k-Ricci曲率之间的关系,推广了Mihai和Özgür的一些结果. 相似文献
7.
Fabio Podestà 《Results in Mathematics》1991,19(1-2):147-156
The notion of affine Kähler immersions has been recently introduced by Nomizu-Pinkall-Podestà ([N-Pi-Po]). This work is aimed at giving some results towards the classification of non degenerate affine Kähler hypersurfaces with symmetric and parallel Ricci tensor; this problem generalizes the classical results due to Nomizu-Smyth ([N-S]) in the theory of Kählerian hypersurfaces. In a second section we deal with the case of “semisymmetric” affine Kähler immersions, when the curvature tensor R satisfies R · R = 0 and the Ricci tensor is symmetric, providing a complete classification; for affine Kähler curves we prove that the conditions above are actually equivalent to saying that the immersion is isometric for a suitable Kähler metric in C2. 相似文献
8.
《中国科学 数学(英文版)》2020,(10)
In this paper, we study locally strongly convex affine hyperspheres in the unimodular affine space R~(n+1) which, as Riemannian manifolds, are locally isometric to the Riemannian product of two Riemannian manifolds both possessing constant sectional curvature. As the main result, a complete classification of such affine hyperspheres is established. Moreover, as direct consequences, 3-and 4-dimensional affine hyperspheres with parallel Ricci tensor are also classified. 相似文献
9.
We consider the motion of hypersurfaces in Riemannian manifolds by their curvature vectors. We show that the Harnack quadratic
is an affine second fundamental form of the space-time track of the hypersurface. Given a solution to the Ricci flow, we show
that with respect to an appropriate metric on space-time, the space-slices evolve by mean curvature flow. This enables us
to identify the Harnack quadratic for the mean curvature flow with the trace Harnack quadratic for the Ricci flow. 相似文献
10.
Ya. M. Chikvashvili 《Mathematical Notes》1969,5(4):245-246
For a function of a field of arbitrary type given in a space of affine connectedness a relationship is deduced which is analogous to the well-known Ricci identity for tensor fields.Translated from Matematicheskie Zametki, Vol. 5, No. 4, pp. 409–411, April, 1969. 相似文献
11.
We investigate the conformally flat semi-Riemannian manifolds withnilpotent Ricci operators. We construct a lot of complete orhomogeneous, conformally flat semi-Riemannian manifolds with nilpotentRicci operators. In this construction, we show interesting relationsbetween the semi-Riemannian geometry and the affine differentialgeometry of centro-affine hypersurfaces. 相似文献
12.
A. De 《Acta Mathematica Hungarica》2009,125(1-2):183-190
The object of the present paper is to study almost pseudo symmetric manifolds admitting a type of semi-symmetric non-metric connection. Also we consider a special conformally flat almost pseudo symmetric manifold admitting a type of semi-symmetric non-metric connection. 相似文献
13.
ON SEMI-SYMMETRIC RECURRENT-METRIC S-CONCIRCULAR CONNECTIONS 总被引:1,自引:0,他引:1
LiangYixing 《数学研究》1994,27(1):104-108
In this paper, the semi-symmetric recurrent-metric S-concircular connec-tion on a Riernannian manifold are defined. Some properties of semi-symmetric recurrent-metric S-concircular connections have been obtained. 相似文献
14.
Abstract. For k ≥ 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not locally affine homogeneous (and hence not
locally homogeneous). All the local scalarWeyl invariants of these manifolds vanish. These manifolds are Ricci flat, Osserman,
and Ivanov-Petrova.
Mathematics Subject Classification (2000): 53B20 相似文献
15.
We establish existence and uniqueness theorems for V-harmonic maps from complete noncompact manifolds. This class of maps includes Hermitian harmonic maps, Weyl harmonic maps, affine harmonic maps, and Finsler harmonic maps from a Finsler manifold into a Riemannian manifold. We also obtain a Liouville type theorem for V-harmonic maps. In addition, we prove a V-Laplacian comparison theorem under the Bakry-Emery Ricci condition. 相似文献
16.
Svatopluk Krýsl 《Monatshefte für Mathematik》2010,161(4):381-398
For a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure), we construct a sequence consisting of differential operators using a symplectic torsion-free affine connection. All but one of these operators are of first order. The first order ones are symplectic analogues of the twistor operators known from Riemannian spin geometry. We prove that under the condition the symplectic Weyl curvature tensor field of the symplectic connection vanishes, the mentioned sequence forms a complex. This gives rise to a new complex for the so called Ricci type symplectic manifolds, which admit a metaplectic structure. 相似文献
17.
Svatopluk Krysl 《Monatshefte für Mathematik》2010,30(2):381-398
For a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure), we construct
a sequence consisting of differential operators using a symplectic torsion-free affine connection. All but one of these operators
are of first order. The first order ones are symplectic analogues of the twistor operators known from Riemannian spin geometry.
We prove that under the condition the symplectic Weyl curvature tensor field of the symplectic connection vanishes, the mentioned
sequence forms a complex. This gives rise to a new complex for the so called Ricci type symplectic manifolds, which admit
a metaplectic structure. 相似文献
18.
Bahaa E. Abdalla Franki Dillen 《Proceedings of the American Mathematical Society》2002,130(6):1805-1808
We construct the first explicit example of a Ricci-semi-symmetric hypersurface of Euclidean space which is not semi-symmetric.
19.
Elif zkara Canfes 《数学物理学报(B辑英文版)》2009,29(1)
In this work,it is proved that every isotropic Weyl manifold with a semi- symmetric connection is locally conformal to an Einstein manifold with a semi-symmetric connection. 相似文献
20.
Dr. S. Muto 《International Journal of Game Theory》1980,9(2):91-97
The concept of semi-symmetric solution for (n, k) games was presented byMuto [1978]. An extension of this type of solution is studied here. 相似文献