In this paper, λ-harmonic maps from a Finsler manifold to a Riemannian manifold are studied. Then, some properties of this kind of harmonic maps are presented and some examples are given. Finally, the stability of the λ-harmonic maps from a Finsler manifold to the standard unit sphere S n (n > 2) is investigated.

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In this paper, we study inverse problem for sprays on Lie algebroids. We obtain necessary and sufficient conditions, based on semi-basic forms, for a spray to be Lagrangian. Then we discuss the Finsler metrizability of a spray and obtain some equations on the Jacobi endomorphism.

In this paper, we extend the Hodge theory to complex Lie algebroids, introduce the Laplacian operators and decompose the cohomological groups with respect to these operators, and generalize Kähler and Nakano identities to Kähler Lie algebroids as well. Our main purpose is to extend Kodaira vanishing theorem to Kähler Lie algebroids.