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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


IMPACT FACTOR 2018: 0.789

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Classification of slant surfaces in 𝕊3 × ℝ

Salvatore de Candia
  • Corresponding author
  • Department of Mathematics, Università degli Studi di Bari, Via E. Orabona n. 4, 70125, Bari, Italy
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/ Marian Ioan Munteanu
Published Online: 2019-09-11 | DOI: https://doi.org/10.1515/advgeom-2019-0019

Abstract

We investigate slant surfaces in the almost Hermitian manifold 𝕊3 × ℝ, considering the position of the Reeb vector field ξ of the Sasakian structure on 𝕊3 with respect to the surfaces. We examine two cases: ξ normal or tangent to the surfaces. In the first case, we prove that every surface is totally real. In the second case, we characterize and locally describe complex surfaces. Finally, we completely classify non-complex slant surfaces, giving explicit examples.

Keywords: Slant surface; almost Hermitian manifold; Sasakian space form

MSC 2010: 53B25; 53C25; 53C15

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About the article

Received: 2018-06-04

Published Online: 2019-09-11


Communicated by: T. Leistner


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2019-0019.

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