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Classification of slant surfaces in π•Š3 Γ— ℝ

  • Salvatore de Candia EMAIL logo and Marian Ioan Munteanu
Published/Copyright: September 11, 2019
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Advances in Geometry
From the journal Advances in Geometry Volume 20 Issue 4

Abstract

We investigate slant surfaces in the almost Hermitian manifold π•Š3 Γ— ℝ, considering the position of the Reeb vector field ΞΎ of the Sasakian structure on π•Š3 with respect to the surfaces. We examine two cases: ΞΎ 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

  1. Communicated by: T. Leistner

Acknowledgements

The first author is a member of the INdAM group GNSAGA.

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Received: 2018-06-04
Published Online: 2019-09-11
Published in Print: 2020-10-27

Β© 2020 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Topology of tropical moduli of weighted stable curves
  3. Classification of slant surfaces in π•Š3 Γ— ℝ
  4. New dense superball packings in three dimensions
  5. Explicit computation of some families of Hurwitz numbers, II
  6. An extension theorem for non-compact split embedded Riemannian symmetric spaces and an application to their universal property
  7. Moduli of stable sheaves supported on curves of genus three contained in a quadric surface
  8. Exceptional points for finitely generated Fuchsian groups of the first kind
  9. Tropical superelliptic curves
  10. Differentiability of projective transformations in dimension 2
  11. On pseudo-Einstein real hypersurfaces
  12. On the moduli spaces of singular principal bundles on stable curves
  13. Three-dimensional connected groups of automorphisms of toroidal circle planes
https://doi.org/10.1515/advgeom-2019-0019
Keywords for this article
Slant surface; almost Hermitian manifold; Sasakian space form

Articles in the same Issue

  1. Frontmatter
  2. Topology of tropical moduli of weighted stable curves
  3. Classification of slant surfaces in π•Š3 Γ— ℝ
  4. New dense superball packings in three dimensions
  5. Explicit computation of some families of Hurwitz numbers, II
  6. An extension theorem for non-compact split embedded Riemannian symmetric spaces and an application to their universal property
  7. Moduli of stable sheaves supported on curves of genus three contained in a quadric surface
  8. Exceptional points for finitely generated Fuchsian groups of the first kind
  9. Tropical superelliptic curves
  10. Differentiability of projective transformations in dimension 2
  11. On pseudo-Einstein real hypersurfaces
  12. On the moduli spaces of singular principal bundles on stable curves
  13. Three-dimensional connected groups of automorphisms of toroidal circle planes
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