Tensor product surfaces with pointwise 1-type gauss map

Abstract

Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle c(1) centered at origin with an Euclidean planar curve c(2) has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle c(1) centered at origin with an Euclidean planar curve c(2) to have pointwise 1-type Gauss map.