In this paper we discuss some results related to angle between Geodesic segments in an infinite dimensional and an asymptotic Teichm¨uller space. Also, we construct a Geodesic triangle in Universal Teichm¨uller space and calculate all of its interior angles

In this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in CAT (0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete Geodesic metric spaces with con- vex metric for which the asymptotic center of a bounded sequence in a bounded closed convex subset is nonempty and singleton. The results obtained in this paper extend and improve some recent results.

In this paper, a novel Patch Geodesic Derivative Pattern (PGDP) describing the texture map of a face through its shape data is proposed. Geodesic adjusted textures are encoded into derivative patterns for similarity measurement between two 3D images with different pose and expression variations. An extensive experimental investigation is conducted using the publicly available Bosphorus and BU-3DFE databases covering face recognition under pose and expression changes. The performance of the proposed method is compared with the performance of the state-of-the-art benchmark approaches. The encouraging experimental results demonstrate that the proposed method is a new solution for 3D face recognition in single model databases.

In this paper, we consider invariant (α, β)-metrics and describe all Geodesic vectors and investigate the set of all homogeneous Geodesics on left invariant hypercomplex four dimensional simply connected Lie groups. Also, we study the conditions for the Douglas and Berwald type of (α, β)-metrics on the left invariant hypercomplex four dimensional simply connected Lie groups.