Semiparallel tensor product surfaces in e 4

Abstract

B.Y. Chen initiated the study of the tensor product immersion of two immersions of a given Riemannian manifold. Inspired by Chen's definition, F. Decruyenaere, F. Dillen, L. Verstraelen and L. Vrancken studied the tensor product of two immersions, in general, different manifolds; under certain conditions, this realizes an immersion of the product manifold. Further, tensor product surfaces of Euclidean plane curves were investigated by I.Mihai and B. Rouxel. In the present study we consider the tensor product surfaces in 4-dimensional Euclidean space E-4. We have shown that tensor product surfaces in E(n)satisfying the semiparallelity condition (R) over bar (X, Y). h = 0 are totally umbilical surfaces.