On the duality between rotational minimal surfaces and maximal surfaces

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Lopez R., Kaya S.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.458, sa.1, ss.345-360, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 458 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.jmaa.2017.09.013
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.345-360
  • Anahtar Kelimeler: Minimal surface, Maximal surface, Weierstrass representation, Bjorling problem, Goursat transformation, CURVATURE, SYSTEMS
  • Ankara Üniversitesi Adresli: Evet

Özet

We investigate the duality between minimal surfaces in Euclidean space and maximal surfaces in Lorentz-Minkowski space in the framework of rotational surfaces. We study if the dual surfaces of two congruent rotational minimal (or maximal) surfaces are congruent. We analyze the duality process when we deform a rotational minimal (maximal) surface by a one-parametric group of rotations. In this context, the family of Bonnet minimal (maximal) surfaces and the Goursat transformations play a remarkable role. (C) 2017 Elsevier Inc. All rights reserved.