Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds

Proceedings Mathematical Sciences

Bayram Sahin¹ 

[1] Department of Mathematics, Inonu University, 0 Malatya, Turkey$$

关键词: Kaehler manifold;    Sasakian manifold;    locally conformal Kaehler manifold;    harmonic map;    Riemannian map;    holomorphic map.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We study harmonic Riemannian maps on locally conformal Kaehler manifolds ($lcK$ manifolds). We show that if a Riemannian holomorphic map between $lcK$ manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we prove that a Riemannian holomorphic map is harmonic if and only if the $lcK$ manifold is Kaehler. Then we find similar results for Riemannian maps between $lcK$ manifolds and Sasakian manifolds. Finally, we check the constancy of some maps between almost complex (or almost contact) manifolds and almost product manifolds.

【 授权许可】

Unknown