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The doubly warped product of holomorphic Lie algebroids. (English) Zbl 1493.53105

Summary: We define the doubly warped product of holomorphic Finsler Lie algebroids. We consider a complex Finsler function and the Chern-Finsler connection of the product bundle and we investigate its relation with the Chern-Finsler connections of each bundle. In the geometrical setting of the prolongations of two Finsler algebroids, we obtain similar and also different properties from the ones of the doubly warped product of Finsler manifolds.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
17B66 Lie algebras of vector fields and related (super) algebras
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
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