Author:

Keywords:

tensor product, minimal surface, Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, 0101 Pure Mathematics, 0102 Applied Mathematics, General Mathematics, 4901 Applied mathematics, 4904 Pure mathematics

Abstract:

The differential geometric study of the tensor product immersion of two Riemannian immersions was initiated by Chen in [2]. In this paper we consider the tensor product immersion of an arbitrary curve in Rm and an arbitrary curve in Rn. We are particularly interested when such a tensor product immersion produces a minimal surface in Euclidean space. In case that m = 2 and n = 2 or n = 3 this question was previously studied in [7] and [1]. Here in the present paper we obtain the general classification result, and at the same time correct some small errors in the results of [1]. © Balkan Society of Geometers, Geometry Balkan Press 2009.