On Doubly Twisted Product of Complex Finsler Manifolds

Xiao, Wei; He, Yong; null, Xiaoying Lu; Deng, Xiangxiang

doi:10.4208/jms.v55n2.22.04

Cited by 7 publications

(7 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Lemma 1 (see [21]). Let (M 1 × (λ 1 ,λ 2 ) M 2 , F) be a doubly twisted product manifold of two strongly pseudoconvex complex Finsler manifolds (M 1 , F 1 ) and (M 2 , F 2 ).…”

Section: Doubly Twisted Product Of Complex Finsler Manifoldsmentioning

confidence: 99%

“…Definition 6 (see [21]). Let (M 1 , F 1 ) and (M 2 , F 2 ) be two strongly pseudoconvex complex Finsler manifolds and λ i : M 1 × M 2 ⟶ (0, +∞)(i � 1, 2) be smooth functions.…”

Section: Doubly Twisted Product Of Complex Finsler Manifoldsmentioning

confidence: 99%

“…Recently, we extended the twisted product to complex Finsler geometry and gave characterization of a doubly twisted product complex Finsler manifold to be Kähler Finsler manifold (resp. weakly Kähler Finsler manifold, complex Berwald manifold, weakly complex Berwald manifold, and complex Landsberg manifold) [21]. Later, we obtained necessary and su cient conditions for a doubly twisted product complex Finsler manifold to be locally dually at [22].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Locally Conformally Flat Doubly Twisted Product Complex Finsler Manifolds

Xiao

Yong

et al. 2022

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

Let M 1 × λ 1 , λ 2 M 2 , F be a doubly twisted product manifold of two strongly pseudoconvex complex Finsler manifolds M 1 , F 1 and M 2 , F 2 . In this study, we give a characterization of locally conformally flat doubly twisted product complex Finsler manifold. We also obtain a necessary and sufficient condition for a doubly twisted product of two locally conformally flat complex Finsler manifolds to be locally conformally flat.

show abstract

“…Lemma 1 (see [21]). Let (M 1 × (λ 1 ,λ 2 ) M 2 , F) be a doubly twisted product manifold of two strongly pseudoconvex complex Finsler manifolds (M 1 , F 1 ) and (M 2 , F 2 ).…”

Section: Doubly Twisted Product Of Complex Finsler Manifoldsmentioning

confidence: 99%

“…Definition 6 (see [21]). Let (M 1 , F 1 ) and (M 2 , F 2 ) be two strongly pseudoconvex complex Finsler manifolds and λ i : M 1 × M 2 ⟶ (0, +∞)(i � 1, 2) be smooth functions.…”

Section: Doubly Twisted Product Of Complex Finsler Manifoldsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Locally Conformally Flat Doubly Twisted Product Complex Finsler Manifolds

Xiao

Yong

et al. 2022

Journal of Mathematics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Kozma, Peter and Shimada [10] extended the twisted product to real Finsler manifolds and studied some geometric properties relating to Cartan connection, geodesic and completeness. Recently, Xiao and He [11] extended the twisted product to complex Finsler manifolds and gave the formulae of holomorphic curvature and Ricci scalar curvature of the doubly twisted product (abbreviated as DTP) complex Finsler manifold. In light of the above results, we shall extend the twisted product to Hermitian manifold, and attempt to derive the Chern curvature, Chern Ricci curvature, Chern Ricci scalar curvature and holomorphic sectional curvature of the twisted product Hermitian manifold.…”

Section: Introductionmentioning

confidence: 99%

Chern Flat and Chern Ricci-Flat Twisted Product Hermitian Manifolds

Li,

He,

et al. 2024

Mathematics

Self Cite

View full text Add to dashboard Cite

Let (M1,g) and (M2,h) be two Hermitian manifolds. The twisted product Hermitian manifold (M1×M2f,G) is the product manifold M1×M2 endowed with the Hermitian metric G=g+f2h, where f is a positive smooth function on M1×M2. In this paper, the Chern curvature, Chern Ricci curvature, Chern Ricci scalar curvature and holomorphic sectional curvature of the twisted product Hermitian manifold are derived. The necessary and sufficient conditions for the compact twisted product Hermitian manifold to have constant holomorphic sectional curvature are obtained. Under the condition that the logarithm of the twisted function is pluriharmonic, it is proved that the twisted product Hermitian manifold is Chern flat or Chern Ricci-flat, if and only if M1,g and M2,h are Chern flat or Chern Ricci-flat, respectively.

show abstract

“…They also gave the necessary and sufficient condition for a compact nontrivial DWP-Hermitian manifold to be of constant holomorphic sectional curvature. Recently, Xiao et al [16] systematically studied holomorphic curvatures of doubly twisted product complex Finsler manifolds, and they [17] gave the necessary and sufficient condition for doubly twisted product complex Finsler manifold to be locally dually flat.…”

Section: Introductionmentioning

confidence: 99%

Levi-Civita Ricci-Flat Doubly Warped Product Hermitian Manifolds

Yong

Yang

et al. 2022

Advances in Mathematical Physics

View full text Add to dashboard Cite

Let M 1 , g and M 2 , h be two Hermitian manifolds. The doubly warped product (abbreviated as DWP) Hermitian manifold of M 1 , g and M 2 , h is the product manifold M 1 × M 2 endowed with the warped product Hermitian metric G = f 2 2 g + f 1 2 h , where f 1 and f 2 are positive smooth functions on M 1 and M 2 , respectively. In this paper, the formulae of Levi-Civita connection, Levi-Civita curvature, the first Levi-Civita Ricci curvature, and Levi-Civita scalar curvature of the DWP-Hermitian manifold are derived in terms of the corresponding objects of its components. We also prove that if the warped function f 1 and f 2 are holomorphic, then the DWP-Hermitian manifold is Levi-Civita Ricci-flat if and only if M 1 , g and M 2 , h are Levi-Civita Ricci-flat manifolds. Thus, we give an effective way to construct Levi-Civita Ricci-flat DWP-Hermitian manifold.

show abstract

On Doubly Twisted Product of Complex Finsler Manifolds

Cited by 7 publications

References 0 publications

Locally Conformally Flat Doubly Twisted Product Complex Finsler Manifolds

Locally Conformally Flat Doubly Twisted Product Complex Finsler Manifolds

Chern Flat and Chern Ricci-Flat Twisted Product Hermitian Manifolds

Levi-Civita Ricci-Flat Doubly Warped Product Hermitian Manifolds

Contact Info

Product

Resources

About