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| 1 | ON DOUBLY WARPED PRODUCT OF COMPLEX FINSLER MANIFOLDS显示文摘Let(M_1,F_1) and(M_2,F_2) be two strongly pseudoconvex complex Finsler manifolds.The doubly wraped product complex Finsler manifold(f_2M_1×f_1 M_2,F) of(M_1,F_1)and(M_2,F_2) is the product manifold M_1×M_2 endowed with the warped product complex Finsler metric F^2 =f_2~2 F_1~2 + f_1~2F_2~2,where f_1 and f_2 are positive smooth functions on M_1 and M2,respectively.In this paper,the most often used complex Finsler connections,holomorphic curvature,Ricci scalar curvature,and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components.Necessary and sufficient conditions for the DWP-complex Finsler manifold to be Kahler Finsler(resp.,weakly Kahler Finsler,complex Berwald,weakly complex Berwald,complex Landsberg) manifold are obtained,respectively.It is proved that if(M_1,F_1) and(M_2,F_2) are projectively flat,then the DWP-complex Finsler manifold is projectively flat if and only if f_1 and f_2 are positive constants. | 何勇 钟春平 | 2016 | Acta Mathematica Scientia2016，36，6： | 3 |
| 2 | On Unitary Invariant Weakly Complex Berwald Metrics with Vanishing Holomorphic Curvature and Closed Geodesics显示文摘In this paper, the authors construct a class of unitary invariant strongly pseudoconvex complex Finsler metrics which are of the form F =√[ rf(s- t)[, where r = ||v||~ 2, s =| z,v |~2/r, t =|| z||~ 2, f(w) is a real-valued smooth positive function of w ∈ R,and z is in a unitary invariant domain M C^n. Complex Finsler metrics of this form are unitary invariant. We prove that F is a class of weakly complex Berwald metrics whose holomorphic curvature and Ricci scalar curvature vanish identically and are independent of the choice of the function f. Under initial value conditions on f and its derivative f, we prove that all the real geodesics of F =√[rf(s- t)] on every Euclidean sphere S^(2n-1) M are great circles. | Hongchuan XIA Chunping ZHONG | 2016 | Chinese Annals of Mathematics,Series B2016，37，2： | 2 |
| 3 | BOCHNER TECHNIQUE ON STRONG KHLER-FINSLER MANIFOLDS显示文摘By using the Chern-Finsler connection and complex Finsler metric,the Bochner technique on strong Khler-Finsler manifolds is studied.For a strong Khler-Finsler manifold M,the authors first prove that there exists a system of local coordinate which is normalized at a point v ∈ M-=T 1,0M\o(M),and then the horizontal Laplace operator H for diffierential forms on PTM is defined by the horizontal part of the Chern-Finsler connection and its curvature tensor,and the horizontal Laplace operator H on holomorphic vector bundle over PTM is also defined.Finally,we get a Bochner vanishing theorem for diffierential forms on PTM.Moreover,the Bochner vanishing theorem on a holomorphic line bundle over PTM is also | 肖金秀 钟同德 邱春晖 | 2010 | Acta Mathematica Scientia2010，30，1： | 1 |
| 4 | 复Kropina度量显示文摘讨论了复Kropina度量成为复Berwald度量的3个不同条件.研究了复Kropina度量的全纯曲率.特别是在β全纯的情况下,得到了复Kropina度量和Hermitian度量之间的全纯曲率关系.找到了复Kropina度量成为复Berwald度量的第4个条件,讨论了迷向全纯曲率. | 汤冬梅 | 2014 | 厦门大学学报(自然科学版)2014，53，2： | 1 |
| 5 | THE MAIN INVARIANTS OF A COMPLEX FINSLER SPACE显示文摘In this paper we extend the results obtained in [3], where are investigated the general settings of the two-dimensional complex Finsler manifolds, with respect to a local complex Berwald frame. The geometry of such manifolds is controlled by three real invariants which live on T ′M : two horizontal curvature invariants K and W and one vertical curvature invariant I. By means of these invariants are defined both the horizontal and the vertical holomorphic sectional curvatures. The complex Landsberg and Berwald spaces are of particular interest. Complex Berwald spaces coincide with K¨ahler spaces, in the two-dimensional case. We establish the necessary and sufficient condition under which K is a constant and we obtain a characterization for the K¨ahler purely Hermitian spaces by the fact K = W = constant and I = 0. For the class of complex Berwald spaces we have K = W = 0.Finally, a classification of two-dimensional complex Finsler spaces for which the horizontal curvature satisfies a special property is obtained. | Nicoleta ALDEA Gheorghe MUNTEANU | 2014 | Acta Mathematica Scientia2014，34，4： | 0 |
| 6 | Bochner-Kodaira Techniques on Kahler Finsler Manifolds显示文摘A horizontal Hodge Laplacian operator □h is defined for Hermitian holomorphic vector bundles over PTM on Khler Finsler manifold,and the expression of □h is obtained explicitly in terms of horizontal covariant derivatives of the Chern-Finsler connection.The vanishing theorem is obtained by using the α_Hα_H-method on Kahler Finsler manifolds. | Jinxiu XIAO Chunhui QIU Tongde ZHONG | 2015 | Chinese Annals of Mathematics,Series B2015，36，1： | 0 |
| 7 | Affinely equivalent Khler-Finsler metrics on a complex manifold显示文摘The purpose of the present paper is to investigate affinely equivalent Khler-Finsler metrics on a complex manifold.We give two facts (1) Projectively equivalent Khler-Finsler metrics must be affinely equivalent;(2) a Khler-Finsler metric is a Khler-Berwald metric if and only if it is affinely equivalent to a Khler metric.Furthermore,we give a formula to describe the affine equivalence of two weakly Khler-Finsler metrics. | YAN RongMu School of Mathematical Science,Xiamen University,Xiamen 361005,China | 2012 | Science China Mathematics2012，55，4： | 0 |
| 8 | 构造具有特殊性质的复Randers度量显示文摘首先证明了当||β||α<1时,复Randers度量的Cartan挠率具有上界.然后推导出所构造的含有3个参数的复Randers度量要么是非弱Khler Finsler度量,要么满足βb0|0+βb0|0≠0,并且该度量具有一致上界.最后给出一些例子说明如果ρ2+λε=0,那么它们的全纯曲率都是非正的. | 汤冬梅 | 2012 | 厦门大学学报(自然科学版)2012，51，2： | 0 |
| 9 | 复流形上强拟凸的复Finsler度量显示文摘复Finsler几何是研究复流形上度量函数没有Hermite二次型限制的Hermite几何,它包括Hermite二次型与非Hermite二次型度量的几何,尤其侧重后者的研究.本文对一些特殊的强拟凸、非Hermite二次型的复Finsler度量的例子作一简单介绍,内容包括复Berwald度量、弱复Berwald度量、Kahler-Finsler度量以及弱Kahler-Finsler度量之间的关系,它们的具体构造及相关分类. | 钟春平 | 2023 | 厦门大学学报(自然科学版)2023，62，6： | 0 |
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