TENSOR PRODUCT SURFACES WITH POINTWISE 1-TYPE GAUSS MAP

ARSLAN K., BULCA B., Kilic B., Kim Y. H., MURATHAN C., Ozturk G.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol.48, no.3, pp.601-609, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.4134/bkms.2011.48.3.601
  • Journal Name: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.601-609
  • Keywords: tensor product immersion, Gauss map, finite type, pointwise 1-type, RULED SURFACES, ROTATION SURFACES
  • Bursa Uludag University Affiliated: Yes

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.