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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: 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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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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Real Hypersurfaces in complex two plane grassmannians with gtw reeb lie derivative structure jacobi operator
Mediterranean Journal of Mathematics, 2016Co-Authors: Eunmi Pak, Gyu Jong Kim, Young Jin SuhAbstract:Using GTW connection, we considered a Real Hypersurface M in a complex two-plane Grassmannian \({G_{2}({\mathbb{C}}^{m+2})}\) when the GTW Reeb Lie derivative of the structure Jacobi operator coincides with the Reeb Lie derivative. Next using the method of simultaneous diagonalization, we prove a complete classification for a Real Hypersurface in \({G_{2}({\mathbb{C}}^{m+2})}\) satisfying such a condition. In this case, we have proved that M is an open part of a tube around a totally geodesic \({G_{2}({\mathbb{C}}^{m+1})}\) in \({G_{2}({\mathbb{C}}^{m+2})}\).
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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.
Wold, Erlend Fornæss - One of the best experts on this subject based on the ideXlab platform.
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Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces
'American Mathematical Society (AMS)', 2018Co-Authors: Deng Fusheng, Fornæss, John Erik, Wold, Erlend FornæssAbstract:We prove that all locally exposable points in a Stein compact in a complex space can be exposed along a given curve to a given Real Hypersurface. Moreover, the exposing map for a boundary point can be sufficiently close to the identity map outside any fixed neighborhood of the point. We also prove a parametric version of this result for bounded strongly pseudoconvex domains in Cn. For a bounded strongly pseudoconvex domain in Cn and a given boundary point of it, we prove that there is a global coordinate change on the closure of the domain which is arbitrarily close to the identity map with respect to the C1 -norm and maps the boundary point to a strongly convex boundary point
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Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces
American Mathematical Society, 2018Co-Authors: Deng Fusheng, Fornæss, John Erik, Wold, Erlend FornæssAbstract:We prove that all locally exposable points in a Stein compact in a complex space can be exposed along a given curve to a given Real Hypersurface. Moreover, the exposing map for a boundary point can be sufficiently close to the identity map outside any fixed neighborhood of the point. We also prove a parametric version of this result for bounded strongly pseudoconvex domains in Cn. For a bounded strongly pseudoconvex domain in Cn and a given boundary point of it, we prove that there is a global coordinate change on the closure of the domain which is arbitrarily close to the identity map with respect to the C1 -norm and maps the boundary point to a strongly convex boundary point.acceptedVersion© 2018. This is the authors' accepted and refereed manuscript to the article. The final authenticated version is available online at: https://doi.org/10.1090/proc/1369
Deng Fusheng - One of the best experts on this subject based on the ideXlab platform.
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Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces
'American Mathematical Society (AMS)', 2018Co-Authors: Deng Fusheng, Fornæss, John Erik, Wold, Erlend FornæssAbstract:We prove that all locally exposable points in a Stein compact in a complex space can be exposed along a given curve to a given Real Hypersurface. Moreover, the exposing map for a boundary point can be sufficiently close to the identity map outside any fixed neighborhood of the point. We also prove a parametric version of this result for bounded strongly pseudoconvex domains in Cn. For a bounded strongly pseudoconvex domain in Cn and a given boundary point of it, we prove that there is a global coordinate change on the closure of the domain which is arbitrarily close to the identity map with respect to the C1 -norm and maps the boundary point to a strongly convex boundary point
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Exposing boundary points of strongly pseudoconvex subvarieties in complex spaces
American Mathematical Society, 2018Co-Authors: Deng Fusheng, Fornæss, John Erik, Wold, Erlend FornæssAbstract:We prove that all locally exposable points in a Stein compact in a complex space can be exposed along a given curve to a given Real Hypersurface. Moreover, the exposing map for a boundary point can be sufficiently close to the identity map outside any fixed neighborhood of the point. We also prove a parametric version of this result for bounded strongly pseudoconvex domains in Cn. For a bounded strongly pseudoconvex domain in Cn and a given boundary point of it, we prove that there is a global coordinate change on the closure of the domain which is arbitrarily close to the identity map with respect to the C1 -norm and maps the boundary point to a strongly convex boundary point.acceptedVersion© 2018. This is the authors' accepted and refereed manuscript to the article. The final authenticated version is available online at: https://doi.org/10.1090/proc/1369
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 generalized tanaka webster reeb parallel shape operator
Monatshefte für Mathematik, 2013Co-Authors: Imsoon Jeong, Makoto Kimura, Hyunjin Lee, 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.
Makoto Kimura - One of the best experts on this subject based on the ideXlab platform.
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Real Hypersurfaces with constant ϕ sectional curvature in complex projective space
Differential Geometry and Its Applications, 2020Co-Authors: Makoto KimuraAbstract:Abstract We will give a geometric description of Real Hypersurfaces with constant ϕ-sectional curvature in complex projective space. Besides geodesic Hypersurfaces, such Real Hypersurfaces are obtained as the image of either a curve or a surface in complex projective space under the polar map. As a consequence, we obtain a classification of Real Hypersurface M 3 in complex projective plane such that the structure vector ξ is an eigenvector of the Ricci tensor.
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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, Makoto Kimura, Hyunjin Lee, 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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ricci solitons and Real Hypersurfaces in a complex space form
Tohoku Mathematical Journal, 2009Co-Authors: Jong Taek Cho, Makoto KimuraAbstract:We prove that a Real Hypersurface in a non-flat complex space form does not admit a Ricci soliton whose potential vector field is the Reeb vector field. Moreover, we classify a Real Hypersurface admitting so-called “η-Ricci soliton” in a non-flat complex space form.
