Surfaces of Revolution With Pointwise 1-Type Gauss Map

Surfaces With Pointwise 1-Type Gauss Map

“…However, the Laplacian of the Gauss map of several important surfaces such as helicoids, catenoids and right cones take a somewhat different form; namely, vector. Otherwise, the pointwise 1-type Gauss map is said to be of the second kind ( [5]). Let M be a surface of Euclidean 3-space E 3 .…”

“…In [5], B.-Y. Chen, M. Choi and Y. H. Kim studied surfaces of revolution with pointwise 1-type Gauss map.…”

Shape Operator and Gauss Map of Pointwise 1-Type

“…for some non-zero smooth function f and a constant vector C. Such a Gauss map is called of pointwise 1-type ( [5,7,9,12,13,14,16]). In particular, if C = 0, it is said to be of pointwise 1-type of the first kind.…”

CLASSIFICATIONS OF HELICOIDAL SURFACES WITH L1-POINTWISE 1-TYPE GAUSS MAP

“…Submanifolds with pointwise 1-type Gauss map have been studied in several papers (cf. [5,10,18,20,22]). …”

“…For example, in [5] and [16], the rotational surfaces of E 3 and E 3 1 with (∆-) pointwise 1-type Gauss map respectively have been studied. Furthermore, several classification theorems on rotational surfaces in E 4 and E 4 2 satisfying (1.2) were given in [14,19,22,23].…”