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Almost Complex Surfaces in the Nearly Kähler SL ( 2 ,ℝ) × SL ( 2 ,ℝ)

Author

Listed:
  • Elsa Ghandour

    (Faculty of Science, University of Lund, Box 118, 2210 Lund, Sweden)

  • Luc Vrancken

    (LMI-Laboratoire de Mathématiques pour l’Ingénieur, Université Polytechnique Hauts-de-France, Campus du Mont Houy, 59313 Valenciennes, France)

Abstract

The space S L ( 2 , R ) × S L ( 2 , R ) admits a natural homogeneous pseudo-Riemannian nearly Kähler structure. We investigate almost complex surfaces in this space. In particular, we obtain a complete classification of the totally geodesic almost complex surfaces and of the almost complex surfaces with parallel second fundamental form.

Suggested Citation

  • Elsa Ghandour & Luc Vrancken, 2020. "Almost Complex Surfaces in the Nearly Kähler SL ( 2 ,ℝ) × SL ( 2 ,ℝ)," Mathematics, MDPI, vol. 8(7), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1160-:d:384866
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