共查询到20条相似文献,搜索用时 937 毫秒
1.
Linfeng Zhou 《Geometriae Dedicata》2012,158(1):353-364
We investigate projective spherically symmetric Finsler metrics with constant flag curvature in R n and give the complete classification theorems. Furthermore, a new class of Finsler metrics with two parameters on n-dimensional disk is found to have constant negative flag curvature. 相似文献
2.
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
3.
In this paper, we investigate the flag curvature of a special class of Finsler metrics called general spherically symmetric Finsler metrics, which are defined by a Euclidean metric and two related 1-forms. We find equations to characterize the class of metrics with constant Ricci curvature (tensor) and constant flag curvature. Moreover, we study general spherically symmetric Finsler metrics with the vanishing non-Riemannian quantity χ-curvature. In particular, we construct some new projectively flat Finsler metrics of constant flag curvature. 相似文献
4.
The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler metrics on an open subset in Rn with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler metric with negative flag curvature and constant S-curvature must be Riemannian if the manifold is compact. We also study the nonpositive flag curvature case.supported by the National Natural Science Foundation of China (10371138). 相似文献
5.
《中国科学 数学(英文版)》2020,(7)
One of the fundamental problems in Finsler geometry is to study Finsler metrics of constant(or scalar) curvature. In this paper, we refine and improve Chen-Shen-Zhao equations characterizing Finsler warped product metrics of scalar flag curvature. In particular, we find equations that characterize Finsler warped product metrics of constant flag curvature. Then we improve the Chen-Shen-Zhao result on characterizing Einstein Finsler warped product metrics. As its application we construct explicitly many new warped product Douglas metrics of constant Ricci curvature by using known locally projectively flat spherically symmetric metrics of constant flag curvature. 相似文献
6.
Xiaohuan Mo 《Results in Mathematics》2011,60(1-4):475-485
(α, β)-norms on ${\mathbb{R}^N}$ induce Minkowski metrics, and the construction of related homothetic vector fields gives a family of new Finsler metrics of non-positive constant flag curvature for each non-trivial (α, β)-norm. The dimension of this family is at least ${\tfrac{1}{2}(N^2 - N + 4)}$ . In particular, we generalize the Funk metric on the unit ball via navigation representation of the standard Euclidean norm and the radial vector field. Finally, we describe the geodesics of these new Finsler metrics with constant flag curvature. 相似文献
7.
In this paper, we study the problem whether a Finsler metric of scalar flag curvature is locally projectively flat. We consider a special class of Finsler metrics — square metrics which are defined by a Riemannian metric and a 1-form on a manifold. We show that in dimension n ≥ 3, any square metric of scalar flag curvature is locally projectively flat. 相似文献
8.
9.
In this paper, we consider a class of Finsler metrics which obtained by Kropina change of the class of generalized m-th root Finsler metrics. We classify projectively flat Finsler metrics in this class of metrics. Then under a condition, we show that every projectively flat Finsler metric in this class with constant flag curvature is locally Minkowskian. Finally, we find necessary and sufficient condition under which this class of metrics be locally dually flat. 相似文献
10.
In this paper we extend the results on projective changes of complex Finsler metrics obtained in Aldea and Munteanu (2012) [3], by the study of projective curvature invariants of a complex Finsler space. By means of these invariants, the notion of complex Douglas space is then defined. A special approach is devoted to the obtaining of equivalence conditions for a complex Finsler space to be a Douglas one. It is shown that any weakly Kähler Douglas space is a complex Berwald space. A projective curvature invariant of Weyl type characterizes complex Berwald spaces. These must be either purely Hermitian of constant holomorphic curvature, or non-purely Hermitian of vanishing holomorphic curvature. Locally projectively flat complex Finsler metrics are also studied. 相似文献
11.
In this paper, we study Finsler metrics of scalar flag curvature. We find that a non-Riemannian quantity is closely related
to the flag curvature. We show that the flag curvature is weakly isotropic if and only if this non-Riemannian quantity takes
a special form. This will lead to a better understanding on Finsler metrics of scalar flag curvature.
相似文献
12.
Xiaohuan Mo 《Results in Mathematics》1999,36(1-2):149-159
13.
In this paper, we give the equivalent PDEs for projectively flat Finsler metrics with constant flag curvature defined by a Euclidean metric and two 1-forms. Furthermore, we construct some classes of new projectively flat Finsler metrics with constant flag curvature by solving these equivalent PDEs. 相似文献
14.
Every Finsler metric induces a spray on a manifold. With a volume form on a manifold, every spray can be deformed to a projective spray. The Ricci curvature of a projective spray is called the projective Ricci curvature. The projective Ricci curvature is an important projective invariant in Finsler geometry. In this paper, we study and characterize projectively Ricci-flat square metrics. Moreover, we construct some nontrivial examples on such Finsler metrics. 相似文献
15.
Xiaohuan Mo 《中国科学A辑(英文版)》1998,41(9):910-917
The geometric characterization and structure of Finsler manifolds with constant flag curvature (CFC) are studied. It is proved
that a Finsler space has constant flag curvature 1 (resp. 0) if and only if the Ricci curvature along the Hilbert form on
the projective sphere bundle attains identically its maximum (resp. Ricci scalar). The horizontal distributionH of this bundle is integrable if and only ifM has zero flag curvature. When a Finsler space has CFC, Hilbert form’s orthogonal complement in the horizontal distribution
is also integrable. Moreover, the minimality of its foliations is equivalent to given Finsler space being Riemannian, and
its first normal space is vertical
Project supported by Wang KC Fundation of Hong Kong and the National Natural Science Foundation of China (Grant No. 19571005). 相似文献
16.
17.
In this paper, we study a class of Finsler metrics in the form
, where
is a Riemannian metric, β = b
i
y
i
is a 1-form, and ε and k ≠ 0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively
flat Finsler metrics with the constant flag curvature must be locally Minkowskian. 相似文献
18.
In this paper we study a special class of Finsler metrics—m-Kropina metrics which are defined by a Riemannian metric and a 1-form. We prove that a weakly Einstein m-Kropina metric must be Einsteinian. Further, we characterize Einstein m-Kropina metrics in very simple conditions under a suitable deformation, and obtain the local structures of m-Kropina metrics which are of constant flag curvature and locally projectively flat with constant flag curvature respectively. 相似文献
19.
Square metrics is an important class of Finsler metrics. Recently, we introduced a special class of non-regular Finsler metrics called singular square metrics. The main purpose of this paper is to provide a necessary and sufficient condition for singular square metrics to be of constant Ricci or flag curvature when dimension . 相似文献
20.
In this paper, we study locally projectively flat Finsler metrics with constant flag curvature K. We prove those are totally determined by their behaviors at the origin by solving some nonlinear PDEs. The classifications when K=0, K=−1 and K=1 are given respectively in an algebraic way. Further, we construct a new projectively flat Finsler metric with flag curvature K=1 determined by a Minkowski norm with double square roots at the origin. As an application of our main theorems, we give the classification of locally projectively flat spherical symmetric Finsler metrics much easier than before. 相似文献