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REAL HYPERSURFACES OF TYPE A IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE NORMAL JACOBI OPERATOR

서영진|Mukut Mani Tripathi|정임순
대한수학회 (The Korean Mathematical Society)|2012.03|대한수학회보 (Bulletin of the KMS)|제49권 제2호|pp. 423-434

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참고문헌

키워드

shape operatorHopf hypersurfacesreal hypersurfacesnormal Jacobi operatorcommuting conditions
주제분류수학

초록

In this paper we give a characterization of real hypersurfaces of type (A) in a complex two-plane Grassmannian $G_2(\mathbb{C}^{m+2})$ which is a tube over a totally geodesic $G_2(\mathbb{C}^{m+1})$ in $G_2(\mathbb{C}^{m+2})$, in terms of two commuting conditions related to the normal Jacobi operator and the shape operator.

Abstract

In this paper we give a characterization of real hypersurfaces of type (A) in a complex two-plane Grassmannian $G_2(\mathbb{C}^{m+2})$ which is a tube over a totally geodesic $G_2(\mathbb{C}^{m+1})$ in $G_2(\mathbb{C}^{m+2})$, in terms of two commuting conditions related to the normal Jacobi operator and the shape operator.

참고문헌 (12)

  1. D. V. Alekseevskii, "Compact quaternion spaces", Func. Anal. Appl, 2, pp.106~114 (1966)
  2. J. Berndt, "Real hypersurfaces in quaternionic space forms", J. Reine Angew. Math, 419, pp.9~26 (1991)
  3. J. Berndt, "Riemannian geometry of complex two-plane Grassmannians", Rend. Sem. Mat. Univ. Politec. Torino, 55(1), pp.19~83 (1997)
  4. J. Berndt, "Real hypersurfaces in complex two-plane Grassmannians", Monatsh. Math, 127(1), pp.1~14 (1999)
  5. J. Berndt, "Real hypersurfaces with isometric Reeb flows in complex two-plane Grassman- nians", Monatsh. Math, 137(2), pp.87~98 (2002)
  6. 정임순, "REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH LIE ξ-PARALLEL NORMAL JACOBI OPERATOR", 대한수학회지, 45(4), pp.1113~1133 (2008), 대한수학회
  7. 이현진, "REAL HYPERSURFACES OF TYPE B IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE REEB VECTOR", 대한수학회보, 47(3), pp.551~561 (2010), 대한수학회
  8. J. D. Perez, "Real hypersurfaces in complex two-plane Grass- mannians with commuting normal Jacobi operator", Acta Math. Hungar, 117(3), pp.201~217 (2007)
  9. Y. J. Suh, "Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator", Bull. Austral. Math. Soc, 67(3), pp.493~502 (2003)
  10. Young Jin Suh, "Real hypersurfaces in complex two-plane Grassmannians with parallel shape operator II", 대한수학회지, 41(3), pp.535~565 (2004), 대한수학회
  11. Y. J. Suh, "Real hypersurfaces in complex two-plane Grassmannians with vanishing Lie derivatives", Canad. Math. Bull, 49(1), pp.134~143 (2006)
  12. Y. J. Suh, "Real hypersurfaces of type B in complex two-plane Grassmannians", Monatsh. Math, 147(4), pp.337~355 (2006)

관련 논문AI추천

Real hypersurfaces in complex two-plane Grassmannians with commuting structure Jacobi operator서영진, 양해영대한수학회 · 대한수학회보2008 · 제45권 제3호REAL HYPERSURFACES OF TYPE B IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE REEB VECTOR서영진, 이현진대한수학회 · 대한수학회보2010 · 제47권 제3호REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH LIE ξ-PARALLEL NORMAL JACOBI OPERATOR서영진, 정임순대한수학회 · 대한수학회지2008 · 제45권 제4호Commuting structure Jacobi operator for Hopf hypersurfaces in complex two-plane Grassmannians서영진, 양해영, 정임순대한수학회 · 대한수학회보2009 · 제46권 제3호Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator서영진, 정임순경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2011 · 제51권 제4호Recurrent Jacobi operator of real hypersurfaces in complex two-plane Grassmannians정임순, Juan de Dios Perez, Young Jin Suh대한수학회 · 대한수학회보2013 · 제50권 제2호

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