Journal of Lie Theory 30 (2020), No. 3, 767--778
Copyright Heldermann Verlag 2020
The Doubly Warped Product of Holomorphic Lie Algebroids
Ana-Maria Ionescu
Faculty of Mathematics and Informatics, Transilvania University, Brasov, Romania
ana.german@unitbv.ro
Alexandru Ionescu
Faculty of Mathematics and Informatics, Transilvania University, Brasov, Romania
alexandru-codrin.ionescu@unitbv.ro
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.
Keywords: Lie algebroid, doubly warped product, prolongation bundle, nonlinear connection, Finsler bundle.
MSC: 17B66, 53B40, 53C60,53D17.
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