Surfaces with parallel mean curvature vector in complex space forms

Dorel Fetcu

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arXiv · 1011.5892

Surfaces with parallel mean curvature vector in complex space forms

Dorel Fetcu

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Abstract

We consider a quadratic form defined on the surfaces with parallel mean curvature vector of an any dimensional complex space form and prove that its $(2,0)$-part is holomorphic. When the complex dimension of the ambient space is equal to $2$ we define a second quadratic form with the same property and then determine those surfaces with parallel mean curvature vector on which the $(2,0)$-parts of both of them vanish. We also provide a reduction of codimension theorem and prove a non-existence result for $2$-spheres with parallel mean curvature vector.

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Dorel Fetcu. 2010-11-25. Surfaces with parallel mean curvature vector in complex space forms. https://arxiv.org/abs/1011.5892

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