SHADOW LEMMA ON FINSLER MANIFOLDS OF HYPERBOLIC TYPE

Let (M, F ) be a compact Finsler manifold of hyperbolic type, ˜MFbe its universal Finslerian covering and αFthe critical exponent of the groupof the deck transformations of ˜F. In this paper we prove the existence of anαF-Busemann quasi-density on the Gromov boundary ˜MG(∞) of ˜. Furthermore, we generalize the Shadow lemma to the compact Finsler manifoldsof hyperbolic type

Keywords:

Finsler manifold, Gromov hyperbolic manifold Busemann quasidensity, Shadow lemma,

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Institut de Math´ematiques et de Sciences Physiques (IMSP),Universit´e d’Abomey- Calavi 01 BP 613 Porto-Novo, Republic of Benin. E-mail address: atincyr@gmail.com E-mail address: ogouyandjou@imsp-uac.org E-mail address: joel.tossa@imsp-uac.org