THE SETS OF POINTS WITH BOUNDED ORBITS FOR GENERALIZED CHEBYSHEV MAPPINGS

2001 ◽  
Vol 11 (01) ◽  
pp. 91-107
Author(s):  
KEISUKE UCHIMURA
Keyword(s):  
Dynamical Systems ◽  
Projective Space ◽  
Complex Variable ◽  
Complex Projective Space ◽  
Cantor Set ◽  
Quadratic Polynomials ◽  
Holomorphic Map ◽  
Simply Connected ◽  
Complex Projective ◽  
Set Of Points

We study the dynamical systems given by generalized Chebyshev mappings [Formula: see text] and show that (1) the set of points with bounded orbits of Fc(z) is connected and its complement in C∪{∞} is simply connected if and only if -4 ≤ c ≤ 2; (2) if c > 2, then the set of points with bounded orbits of Fc(z) is Cantor set. These results are the analogue of the theory of filled Julia sets of quadratic polynomials in one complex variable. We show that the mapping Fc(z) has relation to an important holomorphic map on the complex projective space P2.

Einstein-Kaehler Manifolds Immersed in a Complex Projective Space

1976 ◽  
Vol 28 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Hisao Nakaga
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Local Version ◽  
Kaehler Manifold ◽  
Kaehler Manifolds ◽  
Simply Connected ◽  
Complex Projective

A Kaehler manifold of constant holomorphic curvature is called a complex space form. By a Kaehler submanifold we mean a complex submanifold with the induced Kaehler metric. B. Smyth [5] has studied a complete Einstein- Kaehler hypersurface in a complete and simply connected complex space form and classified completely the hypersurface. The local version of this result has been shown to be true by S. S. Chern [1], and partially by T. Takahashi [6] independently.

Examples of simply-connected K-contact non-Sasakian manifolds of dimension 5

2015 ◽  
Vol 12 (03) ◽  
pp. 1550027 ◽  
Author(s):  
Jin Hong Kim
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Contact Manifold ◽  
Existence Problem ◽  
Sasakian Manifolds ◽  
Contact Manifolds ◽  
Sasakian Structure ◽  
Simply Connected ◽  
Complex Projective

The existence of compact simply-connected K-contact, but not Sasakian, manifolds has been unknown only for dimension 5. The aim of this paper is to show that the Kollár's simply-connected example which is a Seifert bundle over the complex projective space ℂℙ2 and does not carry any Sasakian structure is actually a K-contact manifold. As a consequence, we affirmatively answer the above existence problem in dimension 5, establishing that there are infinitely many compact simply-connected K-contact manifolds of dimension 5 which do not carry a Sasakian structure.

scholarly journals From surfaces in the 5-sphere to 3-manifolds in complex projective 3-space

2002 ◽  
Vol 66 (3) ◽  
pp. 465-475 ◽  
Author(s):  
J. Bolton ◽  
C. Scharlach ◽  
L. Vrancken
Keyword(s):  
Projective Space ◽  
Minimal Surface ◽  
Complex Projective Space ◽  
Lagrangian Submanifold ◽  
3 Dimensional ◽  
Ellipse Of Curvature ◽  
Complex Projective

In a previous paper it was shown how to associate with a Lagrangian submanifold satisfying Chen's equality in 3-dimensional complex projective space, a minimal surface in the 5-sphere with ellipse of curvature a circle. In this paper we focus on the reverse construction.

Reduction theorem of the codimension of minimal generic submanifolds in a complex projective space

1995 ◽  
Vol 54 (2) ◽  
pp. 137-143
Author(s):  
Sung-Baik Lee ◽  
Seung-Gook Han ◽  
Nam-Gil Kim ◽  
Masahiro Kon
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Reduction Theorem ◽  
Generic Submanifolds ◽  
Complex Projective
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