EN
CONTENTS
I. 1. Introduction..................................................................................................................................................................5
2. Preliminaries..............................................................................................................................................................11
3. On Simon’s conjecture..............................................................................................................................................13
II. Pinching theorems for submanifolds of the nearly Kähler 6-sphere..............................................................................16
1. The nearly Kähler structure on S⁶(1)........................................................................................................................16
2. 3-dimensional totally real submanifolds of S⁶............................................................................................................18
3. Totally real surfaces in S⁶..........................................................................................................................................27
III. Surfaces in complex and Sasakian space forms with parallel mean curvature vector...................................................31
1. Totally real surfaces in Kähler manifolds...................................................................................................................31
2. Surfaces of genus 0 with parallel mean curvature vector..........................................................................................34
3. Reduction theorems..................................................................................................................................................51
4. Surfaces of genus 0, C-totally real immersed in Sasakian space forms with parallel mean curvature vector............56
References......................................................................................................................................................................63