Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605952 | Differential Geometry and its Applications | 2014 | 20 Pages |
Abstract
We study pseudo-holomorphic curves in general nearly Kähler manifolds. For that purpose, we first introduce the fundamental equations of submanifold geometry in terms of the characteristic connection of the nearly Kähler structure. Then we classify pseudo-holomorphic curves with parallel second fundamental form in Chern-flat nearly Kähler manifolds. Moreover, we give a new Simons type identity. As an application of this identity, we show that the closed pseudo-holomorphic curves in Chern-flat nearly Kähler manifolds with a second fundamental form of controlled growth are totally geodesic.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Felix Lubbe, Lars Schäfer,