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THE RICCI TENSOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS
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 Title & Authors
THE RICCI TENSOR OF REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS
Perez Juan De Dios; Suh Young-Jin;
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 Abstract
In this paper, first we introduce the full expression of the curvature tensor of a real hypersurface M in complex two-plane Grass-mannians from the equation of Gauss and derive a new formula for the Ricci tensor of M in . Next we prove that there do not exist any Hopf real hypersurfaces in complex two-plane Grassmannians with parallel and commuting Ricci tensor. Finally we show that there do not exist any Einstein Hopf hypersurfaces in .
 Keywords
real hypersurfaces;complex two-plane Grassmannians;parallel Ricci tensor;commuting Ricci tensor;Einstein;
 Language
English
 Cited by
1.
COMMUTING STRUCTURE JACOBI OPERATOR FOR HOPF HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS,;;;

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2.
Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator,;;

Kyungpook mathematical journal, 2011. vol.51. 4, pp.395-410 crossref(new window)
3.
HOPF HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH LIE PARALLEL NORMAL JACOBI OPERATOR,;;;

대한수학회보, 2011. vol.48. 2, pp.427-444 crossref(new window)
4.
REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WHOSE SHAPE OPERATOR IS OF CODAZZI TYPE IN GENERALIZED TANAKA-WEBSTER CONNECTION,;;;

대한수학회보, 2015. vol.52. 1, pp.57-68 crossref(new window)
1.
Real hypersurfaces in complex two-plane Grassmannians with commuting Ricci tensor, Journal of Geometry and Physics, 2010, 60, 11, 1792  crossref(new windwow)
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Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition, Czechoslovak Mathematical Journal, 2012, 62, 3, 849  crossref(new windwow)
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Real hypersurfaces in complex two-plane Grassmannians with Reeb parallel Ricci tensor, Journal of Geometry and Physics, 2013, 64, 1  crossref(new windwow)
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Real hypersurfaces in the complex hyperbolic quadric with Reeb parallel shape operator, Annali di Matematica Pura ed Applicata (1923 -), 2016  crossref(new windwow)
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HOPF HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH LIE PARALLEL NORMAL JACOBI OPERATOR, Bulletin of the Korean Mathematical Society, 2011, 48, 2, 427  crossref(new windwow)
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Real Hypersurfaces in Complex Two-plane Grassmannians with $${\mathfrak{D}^{\bot}}$$ -Parallel Shape Operator, Results in Mathematics, 2013, 64, 3-4, 331  crossref(new windwow)
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Real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator is of Codazzi type, Acta Mathematica Hungarica, 2009, 125, 1-2, 141  crossref(new windwow)
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Ricci Semi-symmetric Hypersurfaces in Complex Two-Plane Grassmannians, Bulletin of the Malaysian Mathematical Sciences Society, 2016  crossref(new windwow)
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Real hypersurfaces in the complex quadric with commuting Ricci tensor, Science China Mathematics, 2016, 59, 11, 2185  crossref(new windwow)
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Pseudo-anti commuting Ricci tensor and Ricci soliton real hypersurfaces in the complex quadric, Journal de Mathématiques Pures et Appliquées, 2016  crossref(new windwow)
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REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH GENERALIZED TANAKA–WEBSTER 𝔇⊥-PARALLEL SHAPE OPERATOR, International Journal of Geometric Methods in Modern Physics, 2012, 09, 04, 1250032  crossref(new windwow)
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REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS SOME OF WHOSE JACOBI OPERATORS ARE ξ-INVARIANT, International Journal of Mathematics, 2012, 23, 03, 1250002  crossref(new windwow)
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Hopf Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Shape Operator, Bulletin of the Malaysian Mathematical Sciences Society, 2015, 38, 2, 617  crossref(new windwow)
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Real Hypersurfaces in Complex Two-Plane Grassmannians Whose Jacobi Operators Corresponding to -Directions are of Codazzi Type, Advances in Pure Mathematics, 2011, 01, 03, 67  crossref(new windwow)
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Real hypersurfaces in the complex quadric with harmonic curvature, Journal de Mathématiques Pures et Appliquées, 2016, 106, 3, 393  crossref(new windwow)
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Real Hypersurfaces in Complex Two-plane Grassmannians with F-parallel Normal Jacobi Operator, Kyungpook mathematical journal, 2011, 51, 4, 395  crossref(new windwow)
18.
Generalized Einstein real hypersurfaces in complex two-plane Grassmannians, Journal of Geometry and Physics, 2010, 60, 11, 1806  crossref(new windwow)
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Addendum to the paper “Real hypersurfaces in complex two-plane Grassmannians with ξ-invariant Ricci tensor”, Journal of Geometry and Physics, 2014, 83, 99  crossref(new windwow)
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Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster Reeb parallel shape operator, Monatshefte für Mathematik, 2013, 171, 3-4, 357  crossref(new windwow)
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Real Hypersurfaces in Complex Hyperbolic Two-Plane Grassmannians with Commuting Structure Jacobi Operators, Mediterranean Journal of Mathematics, 2016, 13, 5, 3389  crossref(new windwow)
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$$\mathfrak D $$ -parallelism of normal and structure Jacobi operators for hypersurfaces in complex two-plane Grassmannians, Annali di Matematica Pura ed Applicata, 2014, 193, 2, 591  crossref(new windwow)
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Real hypersurfaces in complex two-plane Grassmannians with recurrent Ricci tensor, International Journal of Geometric Methods in Modern Physics, 2015, 12, 09, 1550086  crossref(new windwow)
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REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WITH 𝔇⊥-PARALLEL STRUCTURE JACOBI OPERATOR, International Journal of Mathematics, 2011, 22, 05, 655  crossref(new windwow)
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Real hypersurfaces in the complex quadric with commuting and parallel Ricci tensor, Journal of Geometry and Physics, 2016, 106, 130  crossref(new windwow)
26.
Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster $$\mathfrak{D}^ \bot$$-parallel structure Jacobi operator, Open Mathematics, 2014, 12, 12  crossref(new windwow)
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Commuting structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians, Acta Mathematica Sinica, English Series, 2015, 31, 1, 111  crossref(new windwow)
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Real Hypersurfaces in Complex Two-Plane Grassmannians with GTW Reeb Lie Derivative Structure Jacobi Operator, Mediterranean Journal of Mathematics, 2016, 13, 3, 1263  crossref(new windwow)
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On the structure vector field of a real hypersurface in complex two-plane Grassmannians, Central European Journal of Mathematics, 2012, 10, 2, 451  crossref(new windwow)
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Real hypersurfaces in complex two-plane Grassmannians with certain commuting condition II, Czechoslovak Mathematical Journal, 2014, 64, 1, 133  crossref(new windwow)
32.
Real hypersurfaces in the complex quadric with parallel Ricci tensor, Advances in Mathematics, 2015, 281, 886  crossref(new windwow)
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