共查询到20条相似文献,搜索用时 9 毫秒
1.
In this work, it is proved that if a complete Finsler manifold of positive constant Ricci curvature admits a solution to a certain ODE, then it is homeomorphic to the n-sphere. Next, a geometric meaning is obtained for solutions of this ODE, which is applicable to Einstein–Randers spaces. Moreover, some results on Finsler spaces admitting a special conformal vector field are obtained. 相似文献
2.
We study conformal vector fields on a Finsler manifold whose metric is defined by a Riemannian metric, a 1-form and its norm. We find PDEs characterizing conformal vector fields. Then we obtain the explicit expressions of conformal vector fields for certain spherically symmetric metrics on R~n. 相似文献
3.
Huang-jia Tian 《高校应用数学学报(英文版)》2014,29(2):217-229
In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold. 相似文献
4.
Michael Steller 《Annals of Global Analysis and Geometry》2006,29(4):293-311
We study conformal vector fields and their zeros on spacetimes which are non-conformally-flat. Depending on the Petrov type, we classify all conformal vector fields with zeros. The problems of reducing a conformal vector field to a homothetic vector field are considered. We show that a spacetime admitting a proper homothetic vector field is (locally) a plane wave. This precises a well-known theorem of {Alekseevski}, where all these spacetimes are determined in a more general form. 相似文献
5.
S. Deshmukh 《Annali dell'Universita di Ferrara》2011,57(1):17-26
It is known that a conformal vector field on a compact Kaehler manifold is a Killing vector field. In this paper, we are interested
in finding conditions under which a conformal vector field on a non-compact Kaehler manifold is Killing. First we prove that
a harmonic analytic conformal vector field on a 2n-dimensional Kaehler manifold (n ≠ 2) of constant nonzero scalar curvature is Killing. It is also shown that on a 2n-dimensional Kaehler Einstein manifold (n > 1) an analytic conformal vector field is either Killing or else the Kaehler manifold is Ricci flat. In particular, it follows
that on non-flat Kaehler Einstein manifolds of dimension greater than two, analytic conformal vector fields are Killing. 相似文献
6.
In the present paper, we give an answer to a question which is closely related to doubly warped product of Finsler metrics: ‘‘For each n, is there an n-dimensional Finsler manifold , admitting a non-constant smooth function f on M such that ?”. We relate the preceding mentioned condition to different concepts appeared and studied in Finsler geometry. We introduce and investigate the notion of a semi concurrent vector field on a Finsler manifold. We show that some special Finsler manifolds admitting such vector fields turn out to be Riemannian. We prove that Tachibana's characterization of Finsler manifolds admitting a concurrent vector field leads to Riemannian metrics. Various examples for conic Finsler spaces that admit semi-concurrent vector field are presented. 相似文献
7.
8.
In this paper, we investigate the affine vector fields on both compact and forward complete Finsler manifolds. We first give definitions of the affine transformation and the affine vector field. Unexpectedly, we find two kinds of affine fields, which are named as the strongly and weakly affine vector fields. Based on these definitions, we prove some rigidity theorems of affine fields on compact and forward complete Finsler manifolds. 相似文献
9.
We show that in dimension 2 every Finsler metric with at least 3-dimensional Lie algebra of projective vector fields is locally projectively equivalent to a Randers metric. We give a short list of such Finsler metrics which is complete up to coordinate change and projective equivalence. 相似文献
10.
I. G. Shandra 《Journal of Mathematical Sciences》2007,142(5):2419-2435
In this paper, we construct an analogue of concircular fields for semi-Riemannian spaces (i.e., for manifolds with degenerate
metrics). We find a tensor criterion of spaces admitting the maximal number of concircular fields or having no such fields.
We detect a gap in the distribution of dimensions of the space of concircular fields, which, in contrast to the corresponding
gap in the case of pseudo-Riemannian manifolds, is lesser by 1. We also study some special types of concircular fields having
no analogues for pseudo-Riemannian manifolds. The canonical form of the metric for some classes of semi-Riemannian spaces
admitting concircular fields is obtained.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 31, Geometry,
2005. 相似文献
11.
We use a Killing form on a Riemannian manifold to construct a class of Finsler metrics. We find equations that characterize Einstein metrics among this class. In particular, we construct a family of Einstein metrics on S 3 with Ric = 2F 2, Ric = 0 and Ric = -2F 2, respectively. This family of metrics provides an important class of Finsler metrics in dimension three, whose Ricci curvature is a constant, but the flag curvature is not. 相似文献
12.
Let M be an n-dimensional Riemannian manifold and TM its tangent bundle. The conformal and fiber preserving vector fields on TM have well-known physical interpretations and have been studied by physicists and geometers using some Riemannian and pseudo-Riemannian lift metrics on TM. Here we consider the Riemannian or pseudo-Riemannian lift metric G on TM which is in some senses more general than other lift metrics previously defined on TM, and seems to complete these works. Next we study the lift conformal vector fields on (TM,G). 相似文献
13.
14.
Lionel Darondeau 《Mathematische Zeitschrift》2016,282(1-2):547-575
15.
G. S. Asanov 《Journal of Mathematical Sciences》1981,17(1):1610-1624
A systematic survey is given of practically all studies of C-free Finsler spaces. A closed introduction is given and the fundamental theorems are stated. An investigation of projective objects of Finsler spaces with Randers metric is carried out. Physical applications are discussed briefly.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 11, pp. 65–88, 1980. 相似文献
16.
We acknowledge the support by the Swiss National Science Foundation 相似文献
17.
Acta Mathematica Sinica, English Series - In this paper, we study the conformal vector fields on Finsler warped product manifolds. We obtain a system of equivalent equations that the conformal... 相似文献
18.
G. Hoepfner 《Journal of Functional Analysis》2007,247(2):378-416
We characterize the boundary value of homegeneous solutions of planar one-sided locally solvable vector fields with analytic coefficients with the property that the Lp norm of their traces is locally uniformly bounded, 0<p?1. For p≠1/n, , the boundary value must locally belong to the local Hardy space hp(R) of Goldberg while for p=1/n, , the answer calls for a new class of atomic Hardy spaces if the vector field is of infinite type at some boundary point. 相似文献
19.
Giovanni Calvaruso 《Central European Journal of Mathematics》2012,10(2):411-425
Let (M = G/H;g)denote a four-dimensional pseudo-Riemannian generalized symmetric space and g = m + h the corresponding decomposition of
the Lie algebra g of G. We completely determine the harmonicity properties of vector fields belonging to m. In some cases, all these vector fields
are critical points for the energy functional restricted to vector fields. Vector fields defining harmonic maps are also classified,
and the energy of these vector fields is explicitly calculated. 相似文献
20.