On product complex Finsler manifolds

Hongchuan XIA; Qian WEI

Article Details

On product complex Finsler manifolds

Authors:

Hongchuan XIA | Qian WEI

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2019 Vol.43 Issue 1, pp.422-438

Document Type:

Article

Publication Date:

1/2019

Document Language:

Turkish

Document ID (Org No.):

2000745701

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Abstract:

 

Let (M,F)(M,F)(M, F) be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds (M1,F1)(M1,F1)(M_1, F_1) and (M2,F2)(M2,F2)(M_2, F_2) with F=√f(K,H)F=f(K,H)F=\sqrt{f(K, H)} and K=F21K=F12K=F_1^2, H=F22H=F22H=F_2^2. In this paper, we prove that (M,F)(M,F)(M, F) is a weakly Käahler-Finsler (resp. weakly complex Berwald) manifold if and only if (M1,F1)(M1,F1)(M_1, F_1) and (M2,F2)(M2,F2)(M_2, F_2) are both weakly Kähler-Finsler (resp. weakly complex Berwald) manifolds, which is independent of the choice of function fff. Meanwhile, we prove that (M,F)(M,F)(M, F) is a complex Landsberg manifold if and only if either (M1,F1)(M1,F1)(M_1, F_1) and (M2,F2)(M2,F2)(M_2, F_2) are both complex Landsberg manifolds and f=c1K+c2Hf=c1K+c2Hf=c_1K+c_2H with c1,c2c1,c2c_1, c_2 positive constants, or (M1,F1)(M1,F1)(M_1, F_1) and (M2,F2)(M2,F2)(M_2, F_2) are both Kähler-Finsler manifolds.

Article Details

On product complex Finsler manifolds

Authors: Hongchuan XIA | Qian WEI

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2019 Vol.43 Issue 1, pp.422-438

Document Type: Article

Publication Date: 1/2019

Document Language: Turkish

Document ID (Org No.): 2000745701

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Issues

Authors:

Hongchuan XIA | Qian WEI

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2019 Vol.43 Issue 1, pp.422-438

Document Type:

Article

Publication Date:

1/2019

Document Language:

Turkish

Document ID (Org No.):

2000745701

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098