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Biharmonic Submanifolds with Parallel Mean Curvature in \mathbb{S}^{n}\times\mathbb{R} |
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| Authors: | Dorel Fetcu Cezar Oniciuc Harold Rosenberg |
| Institution: | 1. Department of Mathematics and Informatics, Gh. Asachi Technical University of Iasi, Bd. Carol I, 11, 700506, Iasi, Romania 2. Faculty of Mathematics, Al. I. Cuza University of Iasi, Bd. Carol I, 11, 700506, Iasi, Romania 3. IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, Brazil |
| Abstract: | We find a Simons type formula for submanifolds with parallel mean curvature vector (pmc submanifolds) in product spaces M n (c)×?, where M n (c) is a space form with constant sectional curvature c, and then we use it to prove a gap theorem for the mean curvature of certain complete proper-biharmonic pmc submanifolds, and classify proper-biharmonic pmc surfaces in $\mathbb{S}^{n}(c)\times\mathbb{R}$ . |
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