Tensor product surfaces of a Euclidean space curve and a Euclidean plane curve

Abstract

B.Y. Chen initiated the study of the tensor product immersion of two immersions of a given Riemannian manifold (see [3]). Inspired by Chen's definition, F. Decruyenaere, F. Dillen, L. Verstraelen and L. Vrancken (in [4]) studied the tensor product of two immersions of, in general, different manifolds; under certain conditions, this realizes an immersion of the product manifold. In [6] 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. © 2001 Heldermann Verlag.