Constant Mean Curvature Surfaces in $${\mathbb {M}}^2(c)\times \mathbb {R}$$ and Finite Total Curvature |
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Authors: | Márcio Batista Marcos P Cavalcante Dorel Fetcu |
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Institution: | 1.Institute of Mathematics,Federal University of Alagoas,Maceió,Brazil;2.Department of Mathematics and Informatics,Gh. Asachi Technical University of Ia?i,Ia?i,Romania |
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Abstract: | We consider surfaces with parallel mean curvature vector field and finite total curvature in product spaces of type \({\mathbb {M}}^n(c)\times {\mathbb {R}}\), where \({\mathbb {M}}^n(c)\) is a space form and characterize certain of these surfaces. When \(n=2\), our results are similar to those obtained in Bérard et al. (Ann Glob Anal Geom 16(3):273–290, 1998) for surfaces with constant mean curvature in space forms. |
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