Associative submanifolds of squashed 3-Sasakian manifolds

• Gavin Ball ^[1] ; Jesse Madnick ^[2]
  1. [1] University of Missouri

     University of Missouri

     Township of Columbia, Estados Unidos

     
  2. [2] Seton Hall University

     Seton Hall University

     Township of South Orange Village, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 5, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01078-x
• Enlaces
  • Texto completo
• Resumen

  • Every compact 3-Sasakian 7-manifold M admits a canonical 2-parameter family of co-closed G2-structures ϕa,b for a, b > 0, as well as a foliation by ϕa,b-associative 3-folds whose leaf space X is a positive quaternion-Kähler 4-orbifold. We prove that associative 3-folds in (M, ϕa,b) that are ruled by a certain type of geodesic are in correspondence with pseudo-holomorphic curves in the almost-complex 8-manifold Z × S2, where Z is the twistor space of X equipped with its strict nearly-Kähler structure. As an application, we construct infinitely many topological types of nontrivial, compact associative 3-folds in the squashed 7-spheres (S7, ϕa,b) and squashed exceptional Aloff-Wallach spaces (N1,1, ϕa,b). Topologically, our examples are circle bundles over a genus g surface, for any g ≥ 0.

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