Remarks on Kähler–Ricci solitons

2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Lucio Bedulli ◽  
Anna Gori
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Complex Projective Space ◽  
Ricci Soliton ◽  
Compact Complex Manifold ◽  
Ricci Solitons ◽  
Complex Projective

AbstractWe prove that a compact complex manifold endowed with a Kähler-Ricci soliton cannot be isometrically embedded in a complex projective space ℂℙ

HOLOMORPHIC FOLIATIONS AND CHARACTERISTIC NUMBERS

2005 ◽  
Vol 07 (05) ◽  
pp. 583-596 ◽  
Author(s):  
MARCIO G. SOARES
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Complex Projective Space ◽  
Holomorphic Foliation ◽  
Compact Complex Manifold ◽  
Holomorphic Foliations ◽  
Singular Set ◽  
One Dimensional ◽  
Characteristic Numbers ◽  
Complex Projective

We relate the characteristic numbers of the normal sheaf of a k-dimensional holomorphic foliation [Formula: see text] of a compact complex manifold Mn, to the characteristic numbers of the normal sheaf of a one-dimensional holomorphic foliation associated to [Formula: see text]. In case M is a complex projective space, we also obtain bounds for the degrees of the components of codimension k - 1 of the singular set of [Formula: see text].

A Big Picard Theorem for Holomorphic Maps into Complex Projective Space

2009 ◽  
Vol 52 (1) ◽  
pp. 154-160
Author(s):  
Yasheng Ye ◽  
Min Ru
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Complex Projective Space ◽  
Holomorphic Maps ◽  
Analytic Subvariety ◽  
Picard Theorem ◽  
Complex Projective

AbstractWe prove a big Picard type extension theoremfor holomorphic maps f : X–A → M, where X is a complex manifold, A is an analytic subvariety of X, and M is the complement of the union of a set of hyperplanes in ℙn but is not necessarily hyperbolically imbedded in ℙn.

RUANG PROYEKTIF KOMPLEKS 〖CP〗^n ADALAH MANIFOLD KOMPLEKS

2021 ◽  
Vol 9 (1) ◽  
pp. 99
Author(s):  
Denik Agustito ◽  
Irham Taufiq ◽  
Dafid Slamet Setiana ◽  
Riawan Yudi Purwoko
Keyword(s):  
Projective Space ◽  
Complex Manifold ◽  
Research Method ◽  
Compact Manifold ◽  
Complex Projective Space ◽  
Coherent Sheaves ◽  
Complex Projective

<p>The purpose of this paper to determine the complex projective space  as a complex manifold is to calculate the cohomology of the coherent sheaves of . The research method in this paper is to construct an -dimensional complex projective space, namely  and then the n-dimensional complex projective space, namely , is a complex manifold. The result of this research is the -dimensional complex projective space, namely is a complex and compact manifold.</p>

scholarly journals Ricci solitons on CR submanifolds of maximal CR dimension in complex projective space

2016 ◽  
Vol 32 (2) ◽  
pp. 189-193
Author(s):  
MIRCEA CRASMAREANU ◽  
◽  
LAURIAN-IOAN PISCORAN ◽  
Keyword(s):  
Projective Space ◽  
Complex Projective Space ◽  
Second Order ◽  
Ricci Solitons ◽  
Tensor Fields ◽  
Natural Conditions ◽  
Order Tensor ◽  
Complex Projective ◽  
Cr Submanifolds

We study parallel and symmetric second order tensor fields on CR submanifolds of maximal CR dimension of the complex projective space. Under some natural conditions, these tensors are scalar multiples of the metric; an example of submanifold satisfying these assumptions is the geodesic hypersphere. The result is used for Ricci solitons on these CR submanifolds.

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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