Tensor Product Surfaces With Pointwise 1-Type Gauss Map

Abstract

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.

Timelike Factorable Surfaces in Minkowski Space-Time

“…IE 4 Furthermore, in [14], the authors characterized this surface and gave some examples. Also, some surfaces and curves in four dimensinal spaces can be found in [15,16,17,18,19,20,21,22,23,24,25,26,27,28].…”

Homothetic Motion and Surfaces with Pointwise 1-type Gauss Map in $\mathbb E^4$

“…Arslan at el. in [2] gave necessary and sufficent conditions for Vranceanu rotation surface to have pointwise 1-type Gauss map. Yoon in [8] showed that flat Vranceanu rotation surface with pointwise 1-type Gauss map is a Clifford torus.…”

BOOST INVARIANT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN MINKOWSKI 4-SPACE E41

“…Surfaces in Euclidean space and in pseudo-Euclidean space with pointwise 1-type Gauss map were recently studied in [3], [5], [7], [8], [9], [10], [11], [12], [14], [18], [21], [22]. Also Dursun and Turgay in [13] gave all general rotational surfaces in E 4 with proper pointwise 1-type Gauss map of the first kind and classified minimal rotational surfaces with proper pointwise 1-type Gauss map of the second kind.…”

“…Arslan at el. in [2] gave necessary and sufficient conditions for Vranceanu rotation surface to have pointwise 1-type Gauss map. Yoon in [24] showed that flat Vranceanu rotation surface with pointwise 1-type Gauss map is a Clifford torus and in [23] In this paper, we study spacelike surfaces which are invariant under boost transformation (hyperbolic rotations) in Minkowski 4-space.…”