ANNALES POLONICI MATHEMATICI 111.2 (2014) Flat tensor product surfaces of pseudo-Euclidean curves by Adela Mihai and Bogdan Heroiu (Bucure¸sti) Abstract. We determine the flat tensor product surfaces of two curves in pseudo- Euclidean spaces of arbitrary dimensions. 1. Introduction. In [2] B. Y. Chen defined the tensor product of two immersions of a Riemannian manifold and started its study. In [4] the au- thors examined the tensor products of two immersions of, in general, dif- ferent manifolds. I. Mihai and L. Verstraelen [15] gave an overview of the origins of the study of tensor products of submanifolds. As a particular case, the tensor product of two curves results in a tensor product surface. Taking into account some curvature conditions and char- acterizations, many authors studied this topic. In [11], minimal, totally real, complex, slant and pseudo-umbilical ten- sor product surfaces of two Euclidean planar curves are studied (see also [10] and [9]). Classification theorems for minimal, totally real and pseudo- minimal tensor product surfaces of two Lorentzian planar curves are given in [14]. Minimal and pseudo-minimal tensor product surfaces of a Lorentzian planar curve and a Euclidean planar curve are studied in [13]. Recently, in [1] and [6], the authors generalized previous results on mini- mal tensor product surfaces; classification theorems for minimal tensor prod- uct surfaces of two curves in Euclidean and pseudo-Euclidean spaces, respec- tively, of arbitrary dimensions were proved. When the ambient space is a sphere, tensor products are used in [8] to construct examples of Willmore surfaces. It is proved that a surface in a unit sphere which is a tensor product immersion of two curves is flat. To relate this topic to another interesting topic in differential geometry, submanifolds of finite type, we mention that flat tensor product surfaces of two curves of finite type on a unit sphere are surfaces of finite type [3]. 2010 Mathematics Subject Classification : Primary 53C42; Secondary 53A04, 53A07, 53A35. Key words and phrases : flat surface, tensor product surface, pseudo-Euclidean curves. DOI: 10.4064/ap111-2-2 [137] c  Instytut Matematyczny PAN, 2014