I.
1. Introduction
2. Preliminaries
3. On Simon’s conjecture
II. Pinching theorems for submanifolds of the nearly Kähler 6-sphere
1. The nearly Kähler structure on S6(1)
2. 3-dimensional totally real submanifolds of S6
3. Totally real surfaces in S6
III. Surfaces in complex and Sasakian space forms with parallel mean curvature vector
1. Totally real surfaces in Kähler manifolds
2. Surfaces of genus 0 with parallel mean curvature vector
3. Reduction theorems
4. Surfaces of genus 0, C-totally real immersed in Sasakian space forms with parallel mean curvature vector
References