Abstract: B.Y. Chen initiated the study of the tensor product immersion of two immersions of a given Riemannian manifold (see [Ch]). Inspired by Chen's definition, F. Decruyenaere, F. Dillen, L. Verstraelen and L. Vrancken (in [D]) studied the tensor product of two immersions of, in general, different manifolds; under certain conditions, this realizes an immersion of the product manifold. In [M] tensor product surfaces of Euclidean plane curves were investigated. In the present paper, we deal with tensor product surfaces of a Euclidean space curve and a Euclidean plane curve. We classify the minimal, totally real and slant such surfaces, respectively. \item{[Ch]} Chen, B. Y.: Differential Geometry of semiring of immersions, I: General theory. Bull. Inst. Math. Acad. Sinica 21 (1993), 1-34. \item{[D]} Decruyenaere, F.; Dillen, F.; Verstraelen, L.; Vrancken, L.: The semiring of immersions of manifolds. Beiträge Algebra Geom. 34 (1993), 209-215. \item{[M} Mihai, I.; Rosca, R.; Verstraelen, L.; Vrancken, L.: Tensor product surfaces of Euclidean planar curves. Rend. Sem. Mat. Messina 3 (1994/1995), 173-184.
Keywords: Tensor product surfaces, minimal surface, totally real surface, slant surface
Classification (MSC2000): 53C15, 53C40
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