1. Manifolds similar to spheres. 1.1. Let S=S be the w-dimensional sphere, endowed with the usual metric of constant Riemannian curvature 1. Let G=(p(s)), 0^s< oo, be a geodesic ray in S, s being the arc length. Then the conjugate points of £(0) on G occur at S = IT, I a positive integer, with multiplicity n — 1. Let G be a geodesic ray in a Riemannian manifold M=M of dimension n. The following...

Let HC ( ? ) and c denote the classes of sense-preserving harmonic mappings f = h + g ¯ in D with dilation ? z ? for | < 1 such that is Ma–Minda type convex function respect to conjugate points respectively. Here, : ? ? , called function, analytic univalent has positive real part, symmetric axis, starlike 0 > . The are derived from work Sun et al. (2016) on class M ? We study growth theorems fu...