Laplace operators on holomorphic Lie algebroids

Author:

Ionescu Alexandru1

Affiliation:

1. Department of Mathematics and Computer Science, Transilvania University of Braşov, Iuliu Maniu Blvd., 50, 500091 Braşov , Romania

Abstract

Abstract The paper introduces Laplace-type operators for functions defined on the tangent space of a Finsler Lie algebroid, using a volume form on the prolongation of the algebroid. It also presents the construction of a horizontal Laplace operator for forms defined on the prolongation of the algebroid. All the Laplace operators considered in the paper are also locally expressed using the Chern-Finsler connection of the algebroid.

Publisher

Walter de Gruyter GmbH

Reference24 articles.

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2. [2] M. Anastasiei, Geometry of Lagrangians and semisprays on Lie algebroids, BSG Proc., 13, Geom. Balkan Press, Bucharest, p. 10-17, 2006.

3. [3] P.L. Antonelli, B. Lackey, The Theory of Finslerian Laplacians and Applications, Dordrecht, Kluwer Acad. Publ., 459, MAIA, 1998.10.1007/978-94-011-5282-2

4. [4] D. Bao, B. Lackey, A Hodge decomposition theorem for Finsler spaces, C.R. Acad. Sci. Paris, 323, Serie 1, p. 51-56, 1996.

5. [5] C. Ida, Vertical Laplacian on complex Finsler bundles, Acta Math. Acad. Paedagog. Nyhazi.(NS) 26, p. 313-327, 2010.

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2. Vanishing theorems on Kähler Lie algebroids;International Journal of Geometric Methods in Modern Physics;2020-02-26

3. Vanishing Theorems on Holomorphic Lie Algebroids;Mediterranean Journal of Mathematics;2018-11-03

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