TIMELIKE TUBULAR SURFACES OF WEINGARTEN TYPES AND LINEAR WEINGARTEN TYPES IN MINKOWSKI 3-SPACE

Let K, H, KII and HII be the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature of a timelike tubular surface T gamma (alpha) with the radius gamma along a timelike curve alpha(s) in Minkowski 3 -space E13.We prove that T gamma(alpha) must be a (K, H)- Weingarten surface and a (K, H) -linear Weingarten surface. We also show that T gamma(alpha) is (X, Y)-Weingarten type if and only if its central curve is a circle or a helix, where (X, Y ) is an element of {(K, KII), (K, HII), (H, KII), (H, HII), (KII, HII)}. Furthermore, we prove that there exist no timelike tubular surfaces of (X, Y) -linear Weingarten type, (X, Y, Z) -linear Weingarten type and (K, H, KII, HII)-linear Weingarten type along a timelike curve in E13, where (X, Y, Z) is an element of {(K, H, KII), (K, H, HII), (K, KII,HII), (H, KII, HII)}.