• Title, Summary, Keyword: real projective structure

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KILLING STRUCTURE JACOBI OPERATOR OF A REAL HYPERSURFACE IN A COMPLEX PROJECTIVE SPACE

  • Perez, Juan de Dios
    • Journal of the Korean Mathematical Society
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    • v.58 no.2
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    • pp.473-486
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    • 2021
  • We prove non-existence of real hypersurfaces with Killing structure Jacobi operator in complex projective spaces. We also classify real hypersurfaces in complex projective spaces whose structure Jacobi operator is Killing with respect to the k-th generalized Tanaka-Webster connection.

CONVEX DECOMPOSITIONS OF REAL PROJECTIVE SURFACES. III : FOR CLOSED OR NONORIENTABLE SURFACES

  • Park, Suh-Young
    • Journal of the Korean Mathematical Society
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    • v.33 no.4
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    • pp.1139-1171
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    • 1996
  • The purpose of our research is to understand geometric and topological aspects of real projective structures on surfaces. A real projective surface is a differentiable surface with an atlas of charts to $RP^2$ such that transition functions are restrictions of projective automorphisms of $RP^2$. Since such an atlas lifts projective geometry on $RP^2$ to the surface locally and consistently, one can study the global projective geometry of surfaces.

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ON THE FINITENESS OF REAL STRUCTURES OF PROJECTIVE MANIFOLDS

  • Kim, Jin Hong
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.1
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    • pp.109-115
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    • 2020
  • Recently, Lesieutre constructed a 6-dimensional projective variety X over any field of characteristic zero whose automorphism group Aut(X) is discrete but not finitely generated. As an application, he also showed that X is an example of a projective variety with infinitely many non-isomorphic real structures. On the other hand, there are also several finiteness results of real structures of projective varieties. The aim of this short paper is to give a sufficient condition for the finiteness of real structures on a projective manifold in terms of the structure of the automorphism group. To be more precise, in this paper we show that, when X is a projective manifold of any dimension≥ 2, if Aut(X) does not contain a subgroup isomorphic to the non-abelian free group ℤ ∗ ℤ, then there are only finitely many real structures on X, up to ℝ-isomorphisms.

Structure Eigenvectors of the Ricci Tensor in a Real Hypersurface of a Complex Projective Space

  • Li, Chunji;Ki, U-Hang
    • Kyungpook Mathematical Journal
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    • v.46 no.4
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    • pp.463-476
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    • 2006
  • It is known that there are no real hypersurfaces with parallel Ricci tensor in a nonflat complex space form ([6], [9]). In this paper we investigate real hypersurfaces in a complex projective space $P_n\mathbb{C}$ using some conditions of the Ricci tensor S which are weaker than ${\nabla}S=0$. We characterize Hopf hypersurfaces of $P_n\mathbb{C}$.

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Real projective structures on the (2,2,2,2)-orbifold

  • Jun, Jinha
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.535-547
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    • 1997
  • The (2, 2, 2, 2)-orbifold is a 2-dimensional orbifold with four order 2 cone points having 2-sphere as an underlying space. The (2, 2, 2, 2)-orbifold admits different geometric structures. The purpose of this paper is to find some real profective structures on the (2, 2, 2, 2)-orbifold.

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SEMI-INVARIANT SUBMANIFOLDS OF CODIMENSION 3 OF A COMPLEX PROJECTIVE SPACE IN TERMS OF THE JACOBI OPERATOR

  • HER, JONG-IM;KI, U-HANG;LEE, SEONG-BAEK
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.1
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    • pp.93-119
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    • 2005
  • In this paper, we characterize some semi-invariant sub-manifolds of codimension 3 with almost contact metric structure ($\phi$, $\xi$, g) in a complex projective space $CP^{n+1}$ in terms of the structure tensor $\phi$, the Ricci tensor S and the Jacobi operator $R_\xi$ with respect to the structure vector $\xi$.

ITERATIVE FACTORIZATION APPROACH TO PROJECTIVE RECONSTRUCTION FROM UNCALIBRATED IMAGES WITH OCCLUSIONS

  • Shibusawa, Eijiro;Mitsuhashi, Wataru
    • Proceedings of the Korean Society of Broadcast Engineers Conference
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    • pp.737-741
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    • 2009
  • This paper addresses the factorization method to estimate the projective structure of a scene from feature (points) correspondences over images with occlusions. We propose both a column and a row space approaches to estimate the depth parameter using the subspace constraints. The projective depth parameters are estimated by maximizing projection onto the subspace based either on the Joint Projection matrix (JPM) or on the the Joint Structure matrix (JSM). We perform the maximization over significant observation and employ Tardif's Camera Basis Constraints (CBC) method for the matrix factorization, thus the missing data problem can be overcome. The depth estimation and the matrix factorization alternate until convergence is reached. Result of Experiments on both real and synthetic image sequences has confirmed the effectiveness of our proposed method.

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Abstraction of the Real World Using Projective Maps (주관투영도(主觀投影圖)를 활용한 실세계의 추상화)

  • 노태호;최인수
    • Journal of the Korea Society of Computer and Information
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    • v.7 no.1
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    • pp.20-26
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    • 2002
  • Projective Maps let designers find out uncovered attributes which are unexposed by users' incomplete view at abstraction step, and design proper database for users' model This database keeps the original meaning and has a good structure to represent the real world precisely. Also, the database which is designed by using Projective Maps, resents a method which describes the real world by less projections to users.

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