CONTENTSI. 1. Introduction..................................................................................................................................................................5 2. Preliminaries..............................................................................................................................................................11 3. On Simon’s conjecture..............................................................................................................................................13II. 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..........................................................................................................................................27III. 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............56References......................................................................................................................................................................63
1991 Mathematics Subject Classification: Primary 53C20; Secondary 53A10.
@book{bwmeta1.element.dl-catalog-ff798d5e-67b2-452a-8539-d627f8259f47,
author = {Barbara Opozda},
title = {Some contributions to the differential geometry of submanifolds},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1992},
zbl = {0828.53046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.dl-catalog-ff798d5e-67b2-452a-8539-d627f8259f47}
}
Barbara Opozda. Some contributions to the differential geometry of submanifolds. GDML_Books (1992), http://gdmltest.u-ga.fr/item/bwmeta1.element.dl-catalog-ff798d5e-67b2-452a-8539-d627f8259f47/