## Tohoku Mathematical Journal 2016 September SECOND SERIES VOL. 68, NO. 3

 Tohoku Math. J. 68 (2016), 471-486

Title UMBILICAL SURFACES OF PRODUCTS OF SPACE FORMS

Author Jaime Orjuela and Ruy Tojeiro

(Received August 7, 2014, revised February 2, 2015)
Abstract. We give a complete classification of umbilical surfaces of arbitrary codimension of a product $\mathbb{Q}_{k_1}^{n_1}\times \mathbb{Q}_{k_2}^{n_2}$ of space forms whose curvatures satisfy $k_1+k_2\neq 0$.

Mathematics Subject Classification. Primary 53B25; Secondary 53C40.

Key words and phrases. Umbilical surfaces, Riemannian product of space forms.