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.

C o m m u n .Fa c .S c i.U n iv .A n k .S e rie s A 1 Vo lu m e 5 6 , N u m b e r 1 , P a g e s 1 -6 (2 0 0 7 ) IS S N 1 3 0 3 -5 9 9 1 THE DISCRIMINANT OF SECOND FUNDAMENTAL FORM BENGU KILICAbstract. In this study we consider the discriminant of the second fundamental form. As application we also give necessary condition for Vranceanu surface in E 4 to have vanishing discriminant.

In thls .study we consider V-harıııoııic curves and surfaces in Euclidean n-spaces E".We proved that. every weak bihannonic curve is V-harmonic.We also slıowe