D ⊥ -invariant real hypersurfaces in complex Grassmannians of rank two

• Ruenn-Huah Lee ^[1] ; Tee How loo ^[1]
  1. [1] University of Malaya

     University of Malaya

     Malasia

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 61, Nº. 2, 2020, págs. 197-207
• Idioma: inglés
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• Resumen

  • Let M be a real hypersurface in a complex Grassmannian of rank two. Denote by J the quaternionic K¨ahler structure of the ambient space, TM⊥ the normal bundle over M, and D⊥ = JTM⊥. The real hypersurface M is said to be D⊥-invariant if D⊥ is invariant under the shape operator of M. We show that if M is D⊥-invariant, then M is Hopf. This improves the results of Berndt and Suh [Int. J. Math. 23 (2012) 1250103] and [Monatsh. Math. 127 (1999), 1–14]. We also classify D⊥ real hypersurfaces in complex Grassmannians of rank two of noncompact type with constant principal curvatures.