TENSOR PRODUCT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

Title & Authors
TENSOR PRODUCT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP
Arslan, Kadri; Bulca, Betul; Kilic, Bengu; Kim, Young-Ho; Murathan, Cengizhan; Ozturk, Gunay;

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 $\small{c_1}$ centered at origin with an Euclidean planar curve $\small{c_2}$ 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 $\small{c_1}$ centered at origin with an Euclidean planar curve $\small{c_2}$ to have pointwise 1-type Gauss map.
Keywords
tensor product immersion;Gauss map;finite type;pointwise 1-type;
Language
English
Cited by
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2.
FLAT ROTATIONAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN E4,;;

호남수학학술지, 2016. vol.38. 2, pp.305-316
1.
General rotational surfaces with pointwise 1-type Gauss map in pseudo-Euclidean space E 2 4, Indian Journal of Pure and Applied Mathematics, 2015, 46, 1, 107
2.
A study on tensor product surfaces in low-dimensional Euclidean spaces, Ukrainian Mathematical Journal, 2013, 64, 12, 1839
3.
BOOST INVARIANT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN MINKOWSKI 4-SPACE E41, Bulletin of the Korean Mathematical Society, 2014, 51, 6, 1863
4.
FLAT ROTATIONAL SURFACES WITH POINTWISE 1-TYPE GAUSS MAP IN E4, Honam Mathematical Journal, 2016, 38, 2, 305
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