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Young Jin Suh - One of the best experts on this subject based on the ideXlab platform.
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real hypersurfaces in the complex quadric with generalized killing Shape Operator
Journal of Geometry and Physics, 2021Co-Authors: Hyunjin Lee, Doo Hyun Hwang, Young Jin SuhAbstract:Abstract In this paper, we introduce a notion of generalized Killing Shape Operator (or called the quadratic Killing Shape Operator) and its geometric meaning on real hypersurfaces in the complex quadric. In addition, we give a non-existence theorem for a Hopf real hypersurface with generalized Killing Shape Operator in the complex quadric.
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derivatives of the Shape Operator of real hypersurfaces in the complex quadric
Results in Mathematics, 2018Co-Authors: Juan De Dios Perez, Young Jin SuhAbstract:On a real hypersurface in the complex quadric we can consider the Levi-Civita connection and, for any nonnull constant k, the k-th generalized Tanaka-Webster connection. We also have a differential Operator of first order of Lie type associated to the k-th generalized Tanaka-Webster connection. We prove non-existence of real hypersurfaces in the complex quadric for which the covariant derivatives associated to both connections coincide or Lie derivative and Lie type differential Operator coincide when they act on the Shape Operator of the real hypersurface.
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real hypersurfaces with killing Shape Operator in the complex quadric
Mediterranean Journal of Mathematics, 2018Co-Authors: Juan De Dios Perez, Imsoon Jeong, Young Jin SuhAbstract:We introduce the notion of Killing Shape Operator for real hypersurfaces in the complex quadric $$Q^m = SO_{m+2}/SO_mSO_2$$ . The Killing Shape Operator condition implies that the unit normal vector field N becomes $$\mathfrak {A}$$ -principal or $$\mathfrak {A}$$ -isotropic. Then according to each case, we give a complete classification of Hopf real hypersurfaces in $$Q^m = SO_{m+2}/SO_mSO_2$$ with Killing Shape Operator.
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Real hypersurfaces in the complex hyperbolic quadric with Reeb parallel Shape Operator
Annali di Matematica Pura ed Applicata (1923 -), 2017Co-Authors: Young Jin Suh, Doo Hyun HwangAbstract:First, we introduce the notion of Shape Operator of Codazzi type for real hypersurfaces in the complex quadric $${Q^m}^* = SO^{o}_{m,2}/SO_mSO_2$$ Q m ∗ = S O m , 2 o / S O m S O 2 . Next, we give a complete proof of non-existence of real hypersurfaces in $${Q^m}^* = SO^{o}_{m,2}/SO_mSO_2$$ Q m ∗ = S O m , 2 o / S O m S O 2 with Shape Operator of Codazzi type. Motivated by this result, we give a complete classification of real hypersurfaces in $${Q^m}^* = SO^{o}_{m,2}/SO_mSO_2$$ Q m ∗ = S O m , 2 o / S O m S O 2 with Reeb parallel Shape Operator.
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hopf hypersurfaces in complex two plane grassmannians with generalized tanaka webster d parallel Shape Operator
Acta Mathematica Sinica, 2017Co-Authors: Hyunjin Lee, Eunmi Pak, Young Jin SuhAbstract:In this paper, we consider a new notion of generalized Tanaka–Webster D-parallel Shape Operator for a real hypersurface in a complex two-plane Grassmannian and prove a non-existence theorem of a real hypersurface.
Juan De Dios Perez - One of the best experts on this subject based on the ideXlab platform.
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lie derivatives of the Shape Operator of a real hypersurface in a complex projective space
Mediterranean Journal of Mathematics, 2021Co-Authors: Juan De Dios Perez, David PerezlopezAbstract:We consider real hypersurfaces M in complex projective space equipped with both the Levi-Civita and generalized Tanaka–Webster connections. Associated with the generalized Tanaka–Webster connection we can define a differential Operator of first order. For any nonnull real number k and any symmetric tensor field of type (1,1) B on M, we can define a tensor field of type (1,2) on M, $$B^{(k)}_T$$ , related to Lie derivative and such a differential Operator. We study symmetry and skew symmetry of the tensor $$A^{(k)}_T$$ associated with the Shape Operator A of M.
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derivatives of the Shape Operator of real hypersurfaces in the complex quadric
Results in Mathematics, 2018Co-Authors: Juan De Dios Perez, Young Jin SuhAbstract:On a real hypersurface in the complex quadric we can consider the Levi-Civita connection and, for any nonnull constant k, the k-th generalized Tanaka-Webster connection. We also have a differential Operator of first order of Lie type associated to the k-th generalized Tanaka-Webster connection. We prove non-existence of real hypersurfaces in the complex quadric for which the covariant derivatives associated to both connections coincide or Lie derivative and Lie type differential Operator coincide when they act on the Shape Operator of the real hypersurface.
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real hypersurfaces with killing Shape Operator in the complex quadric
Mediterranean Journal of Mathematics, 2018Co-Authors: Juan De Dios Perez, Imsoon Jeong, Young Jin SuhAbstract:We introduce the notion of Killing Shape Operator for real hypersurfaces in the complex quadric $$Q^m = SO_{m+2}/SO_mSO_2$$ . The Killing Shape Operator condition implies that the unit normal vector field N becomes $$\mathfrak {A}$$ -principal or $$\mathfrak {A}$$ -isotropic. Then according to each case, we give a complete classification of Hopf real hypersurfaces in $$Q^m = SO_{m+2}/SO_mSO_2$$ with Killing Shape Operator.
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real hypersurfaces in complex hyperbolic two plane grassmannians with commuting Shape Operator
Open Mathematics, 2015Co-Authors: Juan De Dios Perez, Young Jin Suh, Changhwa WooAbstract:In this paper we prove a non-existence of real hypersurfaces in complex hyperbolic two-plane Grassman- niansSU2;m=S.U2 Um/,m 3, whose structure tensorsf igiD1;2;3 commute with the Shape Operator.
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real hypersurfaces in complex two plane grassmannians whose Shape Operator is recurrent for the generalized tanaka webster connection
Turkish Journal of Mathematics, 2015Co-Authors: Juan De Dios Perez, Young Jin Suh, Changhwa WooAbstract:We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Shape Operator $A$ is generalized Tanaka-Webster recurrent if the principal curvature of the structure vector field is not equal to trace(A).
Changhwa Woo - One of the best experts on this subject based on the ideXlab platform.
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real hypersurfaces in hermitian symmetric space of rank two with killing Shape Operator
2017Co-Authors: Jieun Jang, Young Jin Suh, Changhwa WooAbstract:We have considered a new notion of the Shape Operator A satisfies Killing tensor type for real hypersurfaces M in complex Grassmannians of rank two. With this notion we prove the non-existence of real hypersurfaces M in complex Grassmannians of rank two.
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real hypersurfaces in complex hyperbolic two plane grassmannians with commuting Shape Operator
Open Mathematics, 2015Co-Authors: Juan De Dios Perez, Young Jin Suh, Changhwa WooAbstract:In this paper we prove a non-existence of real hypersurfaces in complex hyperbolic two-plane Grassman- niansSU2;m=S.U2 Um/,m 3, whose structure tensorsf igiD1;2;3 commute with the Shape Operator.
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real hypersurfaces in complex two plane grassmannians whose Shape Operator is recurrent for the generalized tanaka webster connection
Turkish Journal of Mathematics, 2015Co-Authors: Juan De Dios Perez, Young Jin Suh, Changhwa WooAbstract:We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Shape Operator $A$ is generalized Tanaka-Webster recurrent if the principal curvature of the structure vector field is not equal to trace(A).
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hopf hypersurfaces in complex two plane grassmannians with reeb parallel Shape Operator
Bulletin of the Malaysian Mathematical Sciences Society, 2015Co-Authors: Hyunjin Lee, Young Suk Choi, Changhwa WooAbstract:In this paper, we consider a new notion of Reeb parallel Shape Operator for real hypersurfaces $$M$$ in complex two-plane Grassmannians $$G_2({\mathbb C}^{m+2})$$ . When $$M$$ has Reeb parallel Shape Operator and non-vanishing geodesic Reeb flow, it becomes a real hypersurface of Type $$(A)$$ with exactly four distinct constant principal curvatures. Moreover, if $$M$$ has vanishing geodesic Reeb flow and Reeb parallel Shape Operator, then $$M$$ is model space of Type $$(A)$$ with the radius $$r = \frac{\pi }{4\sqrt{2}}$$ .
Hyunjin Lee - One of the best experts on this subject based on the ideXlab platform.
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real hypersurfaces in the complex quadric with generalized killing Shape Operator
Journal of Geometry and Physics, 2021Co-Authors: Hyunjin Lee, Doo Hyun Hwang, Young Jin SuhAbstract:Abstract In this paper, we introduce a notion of generalized Killing Shape Operator (or called the quadratic Killing Shape Operator) and its geometric meaning on real hypersurfaces in the complex quadric. In addition, we give a non-existence theorem for a Hopf real hypersurface with generalized Killing Shape Operator in the complex quadric.
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hopf hypersurfaces in complex two plane grassmannians with generalized tanaka webster d parallel Shape Operator
Acta Mathematica Sinica, 2017Co-Authors: Hyunjin Lee, Eunmi Pak, Young Jin SuhAbstract:In this paper, we consider a new notion of generalized Tanaka–Webster D-parallel Shape Operator for a real hypersurface in a complex two-plane Grassmannian and prove a non-existence theorem of a real hypersurface.
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hopf hypersurfaces in complex two plane grassmannians with mathfrak d parallel Shape Operator
Mathematica Scandinavica, 2015Co-Authors: Hyunjin Lee, Eunmi Pak, Young Jin SuhAbstract:In this paper we consider a generalized condition for Shape Operator of a real hypersurface $M$ in complex two-plane Grassmannian $G_2(\mathsf{C}^{m+2})$, namely, $\mathfrak{D}$-parallel Shape Operator of $M$. Using such a notion, we prove that there does not exist a real hypersurface in complex two-plane Grassmannian $G_2(\mathsf{C}^{m+2})$ with $\mathfrak{D}$-parallel Shape Operator.
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hopf hypersurfaces in complex two plane grassmannians with reeb parallel Shape Operator
Bulletin of the Malaysian Mathematical Sciences Society, 2015Co-Authors: Hyunjin Lee, Young Suk Choi, Changhwa WooAbstract:In this paper, we consider a new notion of Reeb parallel Shape Operator for real hypersurfaces $$M$$ in complex two-plane Grassmannians $$G_2({\mathbb C}^{m+2})$$ . When $$M$$ has Reeb parallel Shape Operator and non-vanishing geodesic Reeb flow, it becomes a real hypersurface of Type $$(A)$$ with exactly four distinct constant principal curvatures. Moreover, if $$M$$ has vanishing geodesic Reeb flow and Reeb parallel Shape Operator, then $$M$$ is model space of Type $$(A)$$ with the radius $$r = \frac{\pi }{4\sqrt{2}}$$ .
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real hypersurfaces in complex two plane grassmannians with mathfrak d bot parallel Shape Operator
Results in Mathematics, 2013Co-Authors: Imsoon Jeong, Hyunjin Lee, Young Jin SuhAbstract:In this paper we consider a new notion of \({\mathfrak{D}^{\bot}}\)-parallel Shape Operator for real hypersurfaces in complex two-plane Grassmannians \({G_2(\mathbb{C}^{m+2})}\) and give a non-existence theorem for a Hopf hypersurface in \({G_2(\mathbb{C}^{m+2})}\) with \({\mathfrak{D}^{\bot}}\)-parallel Shape Operator.
Imsoon Jeong - One of the best experts on this subject based on the ideXlab platform.
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real hypersurfaces with killing Shape Operator in the complex quadric
Mediterranean Journal of Mathematics, 2018Co-Authors: Juan De Dios Perez, Imsoon Jeong, Young Jin SuhAbstract:We introduce the notion of Killing Shape Operator for real hypersurfaces in the complex quadric $$Q^m = SO_{m+2}/SO_mSO_2$$ . The Killing Shape Operator condition implies that the unit normal vector field N becomes $$\mathfrak {A}$$ -principal or $$\mathfrak {A}$$ -isotropic. Then according to each case, we give a complete classification of Hopf real hypersurfaces in $$Q^m = SO_{m+2}/SO_mSO_2$$ with Killing Shape Operator.
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real hypersurfaces in complex two plane grassmannians with mathfrak d bot parallel Shape Operator
Results in Mathematics, 2013Co-Authors: Imsoon Jeong, Hyunjin Lee, Young Jin SuhAbstract:In this paper we consider a new notion of \({\mathfrak{D}^{\bot}}\)-parallel Shape Operator for real hypersurfaces in complex two-plane Grassmannians \({G_2(\mathbb{C}^{m+2})}\) and give a non-existence theorem for a Hopf hypersurface in \({G_2(\mathbb{C}^{m+2})}\) with \({\mathfrak{D}^{\bot}}\)-parallel Shape Operator.
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real hypersurfaces in complex two plane grassmannians with generalized tanaka webster reeb parallel Shape Operator
Monatshefte für Mathematik, 2013Co-Authors: Imsoon Jeong, Hyunjin Lee, Makoto Kimura, Young Jin SuhAbstract:In this paper, we consider a new notion of generalized Tanaka–Webster D-parallel Shape Operator for a real hypersurface in a complex two-plane Grassmannian and prove a non-existence theorem of a real hypersurface.
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real hypersurfaces in complex two plane grassmannians with generalized tanaka webster x1d507 parallel Shape Operator
International Journal of Geometric Methods in Modern Physics, 2012Co-Authors: Imsoon Jeong, Hyunjin Lee, Young Jin SuhAbstract:In a paper due to [I. Jeong, H. Lee and Y. J. Suh, Real hypersurfaces in complex two-plane Grassmannians with generalized Tanaka–Webster parallel Shape Operator, Kodai Math. J.34 (2011) 352–366] we have shown that there does not exist a hypersurface in G2(ℂm+2) with parallel Shape Operator in the generalized Tanaka–Webster connection (see [N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras and Cartan connections, Japan J. Math.20 (1976) 131–190; S. Tanno, Variational problems on contact Riemannian manifolds, Trans. Amer. Math. Soc.314(1) (1989) 349–379]). In this paper, we introduce a new notion of generalized Tanaka–Webster 𝔇⊥-parallel for a hypersurface M in G2(ℂm+2), and give a characterization for a tube around a totally geodesic ℍ Pn in G2(ℂm+2) where m = 2n.
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real hypersurfaces in complex two plane grassmannians with generalized tanaka webster parallel Shape Operator
Kodai Mathematical Journal, 2011Co-Authors: Imsoon Jeong, Hyunjin Lee, Young Jin SuhAbstract:We introduce the notion of generalized Tanaka-Webster connection for hypersurfaces in complex two-plane Grassmannians G2(Cm+2) and give a non-existence theorem for Hopf hypersurfaces in G2(Cm+2) with parallel Shape Operator in this connection.
