الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
This thesis introduce a study of the necessary and sufficient conditions for convexity of subsets in general riemannian manifolds with applications in special types of manifolds such as euclidean, hyperbolic and elliptic spaces.
The whole thesis consists of four chapters, an introduction together with three chapters, which contains the main results we have established.
In chapter, we have quoted the necessary background material for the following three chapters. accordingly, we wrote few sections on manifolds, submanifolds, reimannian manifolds, connexions, convexity and forms , etc, which are important for our study.
In 1990, D.Mejia and D. Minda established the concept of k-convex region with boundary in euclidean 2-space E2. The main aim pf chapter 2 is to define and study the concept of k-convexity of regions in the euclidean 3-space E3.