SHADOW LEMMA ON FINSLER MANIFOLDS OF HYPERBOLIC TYPE

Year 2014, Volume: 2 Issue: 2, 76 - 88, 01.12.2014

CYRIAQUE Atındogbe CARLOSOGOUYANDJOU

https://izlik.org/JA94XC55NN

Abstract

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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