Lagrangian submanifolds of the nearly Kahler S-3 x S-3 from minimal surfaces in S-3

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Atıf İçin Kopyala

Bektaş B., Moruz M., Van der Veken J., Vrancken L.

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, cilt.149, sa.3, ss.655-689, 2019 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 149 Sayı: 3
• Basım Tarihi: 2019
• Doi Numarası: 10.1017/prm.2018.43
• Dergi Adı: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.655-689
• İstanbul Teknik Üniversitesi Adresli: Evet

Özet

We study non-totally geodesic Lagrangian submanifolds of the nearly Kahler S-3 x S-3 for which the projection on the first component is nowhere of maximal rank. We show that this property can be expressed in terms of the so-called angle functions and that such Lagrangian submanifolds are closely related to minimal surfaces in S-3. Indeed, starting from an arbitrary minimal surface, we can construct locally a large family of such Lagrangian immersions, including one exceptional example. We also show that locally all such Lagrangian submanifolds can be obtained in this way.