Real hypersurfaces in complex Grassmannians of rank two with semi-parallel structure Jacobi operator

• Autores: Tee-how Loo de Avik, Changhwa Woo
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 60, Nº. 2, 2019, págs. 505-515
• Idioma: inglés
• DOI: 10.33044/revuma.v60n2a15
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We prove that there does not exist any real hypersurface in complex Grassmannians of rank two with semi-parallel structure Jacobi operator.

    With this result, the non-existence of real hypersurfaces in complex Grassmannians of rank two with recurrent structure Jacobi operator is proved.

• Referencias bibliográficas
  • J. Berndt and Y.J. Suh, Hypersurfaces in noncompact complex Grassmannians of rank two, Internat. J. Math. 23 (2012), no. 10, 1250103, 35 pp....
  • J. Berndt and Y.J. Suh, Real hypersurfaces in complex two-plane Grassmannians, Monatsh. Math. 127 (1999), no. 1, 1–14. MR 1666307.
  • J.T. Cho and M. Kimura, Curvature of Hopf hypersurfaces in a complex space form, Results Math. 61 (2012), no. 1-2, 127–135. MR 2885544.
  • A. De and T.-H. Loo, Pseudo parallel CR-submanifolds in a non-flat complex space form, Taiwanese J. Math. 18 (2014), no. 5, 1549–1562. MR...
  • A. De and T.-H. Loo, Real hypersurfaces with pseudo-parallel normal Jacobi operator in complex two-plane Grassmannians, Filomat 31 (2017),...
  • D.H. Hwang, H. Lee, and C. Woo, Semi-parallel symmetric operators for Hopf hypersurfaces in complex two-plane Grassmannians, Monatsh. Math....
  • T.A. Ivey and P.J. Ryan, The structure Jacobi operator for hypersurfaces in CP2 and CH2, Results Math. 56 (2009), no. 1-4, 473–488. MR 2575873.
  • I. Jeong, S. Kim, and Y.J. Suh, Real hypersurfaces in complex two-plane Grassmannians with Reeb parallel structure Jacobi operator, Canad....
  • I. Jeong, C.J.G. Machado, J.D. P´erez, and Y.J. Suh, Real hypersurfaces in complex two-plane Grassmannians with D⊥-parallel structure Jacobi...
  • I. Jeong, J.D. P´erez, Y.J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel structure Jacobi operator, Acta Math....
  • I. Jeong, Y.J. Suh, and C. Woo, Real hypersurfaces in complex two-plane Grassmannians with recurrent structure Jacobi operator, in: Real and...
  • R.-H. Lee and T.-H. Loo, Hopf hypersurfaces in complex Grassmannians of rank two, Results Math. 71 (2017), no. 3-4, 1083–1107. MR 3648463.
  • T.-H. Loo, Semi-parallel real hypersurfaces in complex two-plane Grassmannians, Differ. Geom. Appl. 34 (2014), 87–102. MR 3209539.
  • C.J.G. Machado, J.D. P´erez, Y.J. Suh, Commuting structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians, Acta...
  • Y.J. Suh and C. Woo, Real hypersurfaces in complex hyperbolic two-plane Grassmannians with parallel Ricci tensor, Math. Nachr. 287 (2014),...
  • Y.J. Suh, Real hypersurfaces in complex two-plane Grassmannians with parallel Ricci tensor, Proc. Roy. Soc. Edinburgh Sect. A 142 (2012),...