Tensor product surfaces with pointwise 1-type Gauss map
Bull. Korean Math. Soc. 2011 Vol. 48, No. 3, 601-609
https://doi.org/10.4134/BKMS.2011.48.3.601
Published online May 1, 2011
Kadri Arslan, Bet\"{u}l Bulca, Beng\"{u} K\i l\i \c{c}, Young Ho Kim, Cengizhan Murathan, and G\"{u}nay \"{O}zt\"{u}rk
Uluda\u{g} University, Uluda\u{g} University, Bal\i kesir University, Kyungpook National University, Uluda\u{g} University, Kocaeli University
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.
Keywords : tensor product immersion, Gauss map, finite type, pointwise 1-type
MSC numbers : 53C40, 53C42
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