Laplacians for the holomorphic tangent bundles with g-nature metrics on complex Finsler manifolds
Keyword(s):
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].
2012 ◽
Vol 09
(07)
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pp. 1250061
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2003 ◽
Vol 27
(2)
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pp. 295-306
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Keyword(s):
2019 ◽
Vol 16
(11)
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pp. 1950180
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