Hongchuan XIA, Qian WEI

8287

On product complex Finsler manifolds

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 $F=\sqrt{f(K, H)}$ and $K=F_1^2$, $H=F_2^2$. In this paper, we prove that $(M, F)$ is a weakly Käahler-Finsler (resp. weakly complex Berwald) manifold if and only if $(M_1, F_1)$ and $(M_2, F_2)$ are both weakly Kähler-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 $f=c_1K+c_2H$ with $c_1, c_2$ positive constants, or $(M_1, F_1)$ and $(M_2, F_2)$ are both Kähler-Finsler manifolds.
Keywords:

Product manifold, weakly complex Berwald manifold weakly Kähler-Finsler manifold, complex Landsberg manifold,

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Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: 6
  • Yayıncı: TÜBİTAK
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