**
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 2, pp. 523-530 (2001)
**

#
Tensor Product Surfaces of a Euclidean Space Curve and a Euclidean Plane Curve

##
Kadri Arslan, Ridvan Ezentas, Ion Mihai, Cengizhan Murathan, Cihan Özgür

Department of Mathematics, Faculty of Art and Sciences, Uludag University, Görükle 16059, Bursa, Turkey (authors 1, 2, 4, 5); Faculty of Mathematics, Str. Academiei 14, 70109 Bucharest, Romania (author 3)

**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

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2001 ELibM for
the EMIS Electronic Edition
*