On product complex Finsler manifolds

被引：6

作者：

Xia, Hongchuan ^{[1
]}

Wei, Qian ^{[1
]}

机构：

[1] Xinyang Normal Univ, Sch Math & Stat, Xinyang, Peoples R China

来源：

TURKISH JOURNAL OF MATHEMATICS | 2019年 / 43卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Product manifold; weakly complex Berwald manifold; weakly Kahler-Finsler manifold; complex Landsberg manifold; BERWALD METRICS;

D O I：

10.3906/mat-1809-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (M, F) be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds (M-1, F-1) and (M-2, F-2) with F = root f (K, H) and K = F-1(2), H = F-2(2). In this paper, we prove that (M, F) is a weakly Kahler-Finsler (resp. weakly complex Berwald) manifold if and only if (M-1, F-1) and (M-2, F-2) are both weakly Kahler- Finsler (resp. weakly complex Berwald) manifolds, which is independent of the choice of function f . Meanwhile, we prove that (M, F) is a complex Landsberg manifold if and only if either (M-1, F-1) and (M-2, F-2) are both complex Landsberg manifolds and f = c(1)K + c(2)H with c(l), c(2) positive constants, or (M-1, F-1) and (M-2, F-2) are both Kahler- Finsler manifolds.

引用

页码：422 / 438

页数：17