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TENSOR PRODUCT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP
Arslan, Kadri,Bulca, Betul,Kilic, Bengu,Kim, Young-Ho,Murathan, Cengizhan,Ozturk, Gunay Korean Mathematical Society 2011 대한수학회보 Vol.48 No.3
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.
Tensor product surfaces with pointwise 1-type Gauss map
Kadri Arslan,Betul Bulca,Bengu Kilic,Young Ho Kim,Cengizhan Murathan,Gunay Ozturk 대한수학회 2011 대한수학회보 Vol.48 No.3
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.