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