Schwarz lemma and Hartogs phenomenon in complex Finsler manifold

2013 ◽  
Vol 34 (3) ◽  
pp. 455-460 ◽  
Author(s):  
Bin Shen ◽  
Yibing Shen
Keyword(s):  
Finsler Manifold ◽  
Schwarz Lemma ◽  
Complex Finsler Manifold ◽  
Hartogs Phenomenon

Laplacians for the holomorphic tangent bundles with g-nature metrics on complex Finsler manifolds

2017 ◽  
Vol 28 (09) ◽  
pp. 1740011
Author(s):  
Hongjun Li ◽  
Chunhui Qiu ◽  
Weixia Zhu
Keyword(s):  
Laplace Operator ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Killing Vector ◽  
Finsler Manifold ◽  
Killing Vector Fields ◽  
Finsler Manifolds ◽  
Complex Finsler Manifold ◽  
Precise Relationship ◽  
Tangent Bundles

Let [Formula: see text] be a strongly pseudoconvex compact complex Finsler manifold. We first introduce a class of [Formula: see text]-nature metric [Formula: see text] for the slit holomorphic tangent bundle [Formula: see text] on [Formula: see text]. Then, we define the complex horizontal Laplacian [Formula: see text], and complex vertical Laplacian [Formula: see text], and obtain a precise relationship among [Formula: see text], [Formula: see text] and the Hodge–Laplace operator [Formula: see text] on [Formula: see text]. As an application, we discuss the holomorphic Killing vector fields associated to [Formula: see text].

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