Surfaces with parallel mean curvature in Sasakian space forms

Dorel Fetcu; Harold Rosenberg

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arXiv · 1308.6827

Surfaces with parallel mean curvature in Sasakian space forms

Dorel Fetcu·Harold Rosenberg

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Abstract

We study the global geometry of surfaces in Sasakian space forms whose mean curvature vector is parallel in the normal bundle (these include the Riemannian Heisenberg space of dimension $2n+1$). We prove a codimension reduction theorem. We introduce two holomorphic quadratic differentials on anti-invariant such surfaces and use them to obtain classification theorems.

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Dorel Fetcu, Harold Rosenberg. 2013-08-30. Surfaces with parallel mean curvature in Sasakian space forms. https://arxiv.org/abs/1308.6827

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