Revista Matemática Iberoamericana


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Volume 29, Issue 4, 2013, pp. 1283–1306
DOI: 10.4171/RMI/757

Published online: 2013-12-15

On complete submanifolds with parallel mean curvature in product spaces

Dorel Fetcu[1] and Harold Rosenberg[2]

(1) Universitatea Tehnică “Gheorghe Asachi” din Iaşi, Romania
(2) Rio de Janeiro, Brazil

We prove a Simons type formula for submanifolds with parallel mean curvature vector field in product spaces of type $M^n(c)\times\mathbb{R}$, where $M^n(c)$ is a space form with constant sectional curvature $c$, and then we use it to characterize some of these submanifolds.

Keywords: Submanifolds with parallel mean curvature vector field, Simons type equation

Fetcu Dorel, Rosenberg Harold: On complete submanifolds with parallel mean curvature in product spaces. Rev. Mat. Iberoamericana 29 (2013), 1283-1306. doi: 10.4171/RMI/757