Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2011; 48(3): 601-609

Printed May 1, 2011

https://doi.org/10.4134/BKMS.2011.48.3.601

Copyright © The Korean Mathematical Society.

Tensor product surfaces with pointwise 1-type Gauss map

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