Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników

Czasopismo

2014 | 12 | 12 | 1840-1851

Tytuł artykułu

Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster $$\mathfrak{D}^ \bot$$-parallel structure Jacobi operator

Autorzy

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
Regarding the generalized Tanaka-Webster connection, we considered a new notion of $$\mathfrak{D}^ \bot$$-parallel structure Jacobi operator for a real hypersurface in a complex two-plane Grassmannian G 2(ℂm+2) and proved that a real hypersurface in G 2(ℂm+2) with generalized Tanaka-Webster $$\mathfrak{D}^ \bot$$-parallel structure Jacobi operator is locally congruent to an open part of a tube around a totally geodesic quaternionic projective space ℍP n in G 2(ℂm+2), where m = 2n.

Wydawca

Czasopismo

Rocznik

Tom

12

Numer

12

Strony

1840-1851

Opis fizyczny

Daty

wydano
2014-12-01
online
2014-07-20

Twórcy

autor
  • Kyungpook National University
autor
  • Kyungpook National University

Bibliografia

  • [1] Alekseevskii D. V., Compact quaternion spaces, Funct. Anal. Appl., 1968, 2, 11–20
  • [2] Berndt J., Riemannian geometry of complex two-plane Grassmannian, Rend. Sem. Mat. Univ. Politec. Torino, 1997, 55, 19–83
  • [3] Berndt J. and Suh Y. J., Real hypersurfaces in complex two-plane Grassmannians, Monatsh. Math., 1999, 127, 1–14 http://dx.doi.org/10.1007/s006050050018
  • [4] Berndt J. and Suh Y. J., Real hypersurfaces with isometric Reeb flow in complex two-plane Grassmannians, Monatsh. Math., 2002, 137, 87–98 http://dx.doi.org/10.1007/s00605-001-0494-4
  • [5] Jeong I., Pérez J. D. and Suh Y. J., Real hypersurfaces in complex two-plane Grassmannians with parallel structure Jacobi operator, Acta Math. Hungar., 2009, 122, 173–186 http://dx.doi.org/10.1007/s10474-008-8004-y
  • [6] Jeong I., Machado C. J. G., Pérez J. D. and Suh Y. J., Real hypersurfaces in complex two-plane Grassmannians with \(\mathfrak{D}^ \bot\) -parallel structure Jacobi operator, Internat. J. Math., 2011, 22, 655–673 http://dx.doi.org/10.1142/S0129167X11006957
  • [7] Ki U-H., Pérez J. D., Santos F. G. and Suh Y. J., Real hypersurfaces in complex space forms with ξ-parallel Ricci tensor and structure Jacobi operator, J. Korean Math. Soc., 2007, 44, 307–326 http://dx.doi.org/10.4134/JKMS.2007.44.2.307
  • [8] Kon M., Real hypersurfaces in complex space forms and the generalized-Tanaka-Webster connection, Proceeding of the 13th International Workshop on Differential Geometry anad Related Fields (5–7 Nov. 2009 Taegu Republic of Korea), National Institute of Mathematical Sciences, 2009, 145–159
  • [9] Lee H. and Suh Y. J., Real hypersurfaces of type B in complex two-plane Grassmannians related to the Reeb vector, Bull. Korean Math. Soc., 2010, 47, 551–561 http://dx.doi.org/10.4134/BKMS.2010.47.3.551
  • [10] Pak E. and Suh Y. J., Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster Reeb parallel structure Jacobi operator, (Submitted)
  • [11] Pérez J. D., Santos F. G. and Suh Y. J., Real hypersurfaces in complex projective space whose structure Jacobi operator is D-parallel, Bull. Belg. Math. Soc. Simon Stevin, 2006, 13, 459–469
  • [12] Pérez J. D. and Suh Y. J., Real hypersurfaces of quaternionic projective space satisfying \(\nabla _{U_t } R = 0\) , Differential Geom. Appl., 1997, 7, 211–217 http://dx.doi.org/10.1016/S0926-2245(97)00003-X
  • [13] Pérez J. D. and Suh Y. J., The Ricci tensor of real hypersurfaces in complex two-plane Grassmannians, J. Korean Math. Soc., 2007, 44, 211–235 http://dx.doi.org/10.4134/JKMS.2007.44.1.211
  • [14] Pérez J. D., Suh Y. J. and Watanabe Y., Generalized Einstein real hypersurfaces in complex two-plane Grassmannians, J. Geom. Phys., 2010, 60, 1806–1818 http://dx.doi.org/10.1016/j.geomphys.2010.06.017
  • [15] Suh Y. J., Real hypersurfaces in complex two-plane Grassmannians with ξ-invariant Ricci tensor, J. Geom. Phys., 2011, 61, 808–814 http://dx.doi.org/10.1016/j.geomphys.2010.12.010
  • [16] Suh Y. J., Real hypersurfaces in complex two-plane Grassmannians with parallel Ricci tensor, Proc. Roy. Soc. Edinburgh Sect. A., 2012, 142, 1309–1324 http://dx.doi.org/10.1017/S0308210510001472
  • [17] Suh Y. J., Real hypersurfaces in complex two-plane Grassmannians with Reeb parallel Ricci tensor, J. Geom. Phys., 2013, 64, 1–11 http://dx.doi.org/10.1016/j.geomphys.2012.10.005
  • [18] Suh Y. J., Real hypersurfaces in complex two-plane Grassmannians with harmonic curvature, J. Math. Pures Appl., 2013, 100, 16–33 http://dx.doi.org/10.1016/j.matpur.2012.10.010
  • [19] Tanaka N., On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Jpn. J. Math., 1976, 2, 131–190
  • [20] Tanno S., Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc., 1989, 314, 349–379 http://dx.doi.org/10.1090/S0002-9947-1989-1000553-9
  • [21] Webster S.M., Pseudo-Hermitian structures on a real hypersurface, J. Differential Geom., 1978, 13, 25–41

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_2478_s11533-014-0447-5
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.