Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 26, No. 2, pp. 313-327 (2010)

Vertical Laplacian on complex Finsler bundles

Cristian Ida

Transilvania University of Brasov

Abstract: In this paper we define vertical and horizontal Laplace type operators for functions on the total space of a complex Finsler bundle $(E,L)$. We also define the Laplacian for $(p,q,r,s)$-forms with compact support on $E$ and we get the local expression of this Laplacian explicitly in terms of vertical covariant derivatives with respect to the Chern-Finsler linear connection of $(E,L)$.

Keywords: complex Finsler bundles, vertical Laplacian

Classification (MSC2000): 53B40; 53B35, 53B21

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