scholarly journals Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology

2000 ◽  
Vol 352 (12) ◽  
pp. 5405-5433 ◽  
Author(s):  
Luis A. Cordero ◽  
Marisa Fernández ◽  
Alfred Gray ◽  
Luis Ugarte
Keyword(s):  
Complex Structures ◽  
Dolbeault Cohomology ◽  
Compact Nilmanifolds

scholarly journals Remarks on Hodge numbers and invariant complex structures of compact nilmanifolds

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Takumi Yamada
Keyword(s):  
Lie Group ◽  
Complex Structure ◽  
Complex Structures ◽  
Nilpotent Lie Group ◽  
Hodge Numbers ◽  
Compact Nilmanifolds ◽  
Simply Connected

AbstractIf N is a simply connected real nilpotent Lie group with a Γ-rational complex structure, where Γ is a lattice in N, then for each s, t.We study relations between invariant complex structures and Hodge numbers of compact nilmanifolds from a viewpoint of Lie algberas.

scholarly journals Hodge numbers and invariant complex structures of compact nilmanifolds

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Takumi Yamada
Keyword(s):  
Complex Structures ◽  
Hodge Numbers ◽  
Compact Nilmanifolds

AbstractIn this paper, we consider several invariant complex structures on a compact real nilmanifold, and we study relations between invariant complex structures and Hodge numbers.

scholarly journals Holomorphic Poisson Cohomology

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Zhuo Chen ◽  
Daniele Grandini ◽  
Yat-Sun Poon
Keyword(s):  
Spectral Sequence ◽  
Complex Structure ◽  
Complex Structures ◽  
Dolbeault Cohomology ◽  
Double Complex ◽  
Poisson Cohomology ◽  
Compact Complex Surfaces ◽  
Generalized Geometry ◽  
Holomorphic Poisson Cohomology ◽  
Compact Complex Manifolds

AbstractHolomorphic Poisson structures arise naturally in the realm of generalized geometry. A holomorphic Poisson structure induces a deformation of the complex structure in a generalized sense, whose cohomology is obtained by twisting the Dolbeault @-operator by the holomorphic Poisson bivector field. Therefore, the cohomology space naturally appears as the limit of a spectral sequence of a double complex. The first sheet of this spectral sequence is simply the Dolbeault cohomology with coefficients in the exterior algebra of the holomorphic tangent bundle. We identify various necessary conditions on compact complex manifolds on which this spectral sequence degenerates on the level of the second sheet. The manifolds to our concern include all compact complex surfaces, Kähler manifolds, and nilmanifolds with abelian complex structures or parallelizable complex structures.

scholarly journals Dolbeault cohomology of compact nilmanifolds

2001 ◽  
Vol 6 (2) ◽  
pp. 111-124 ◽  
Author(s):  
S. Console ◽  
A. Fino
Keyword(s):  
Dolbeault Cohomology ◽  
Compact Nilmanifolds

scholarly journals Some relations between Hodge numbers and invariant complex structures on compact nilmanifolds

2017 ◽  
Vol 4 (1) ◽  
pp. 73-83
Author(s):  
Takumi Yamada
Keyword(s):  
Lie Algebra ◽  
Lie Group ◽  
Complex Structure ◽  
Complex Structures ◽  
Nilpotent Lie Group ◽  
Hodge Numbers ◽  
Compact Nilmanifolds ◽  
Simply Connected ◽  
Invariant Complex Structure

AbstractLet N be a simply connected real nilpotent Lie group, n its Lie algebra, and € a lattice in N. If a left-invariant complex structure on N is Γ-rational, then HƏ̄s,t(Γ/N) ≃ HƏ̄s,t(nC) for each s; t. We can construct different left-invariant complex structures on one nilpotent Lie group by using the complexification and the scalar restriction. We investigate relationships to Hodge numbers of associated compact complex nilmanifolds.

Cell morphology, volume, and surface area determinations from multilevel contouring within HVEM micrographs of serial sections and whole-cell mounts

1987 ◽  
Vol 45 ◽  
pp. 588-589
Author(s):  
M. Marko ◽  
A. Leith ◽  
D. Parsons
Keyword(s):  
Surface Area ◽  
Electron Micrographs ◽  
Cell Morphology ◽  
Individual Variation ◽  
Serial Section ◽  
Stereo Pair ◽  
Complex Structures ◽  
Serial Sections ◽  
Surface Areas ◽  
Computer Based

The use of serial sections and computer-based 3-D reconstruction techniques affords an opportunity not only to visualize the shape and distribution of the structures being studied, but also to determine their volumes and surface areas. Up until now, this has been done using serial ultrathin sections.The serial-section approach differs from the stereo logical methods of Weibel in that it is based on the Information from a set of single, complete cells (or organelles) rather than on a random 2-dimensional sampling of a population of cells. Because of this, it can more easily provide absolute values of volume and surface area, especially for highly-complex structures. It also allows study of individual variation among the cells, and study of structures which occur only infrequently.We have developed a system for 3-D reconstruction of objects from stereo-pair electron micrographs of thick specimens.

Stereo modeling of HVEM specimens by serial tilting and computer graphics

1986 ◽  
Vol 44 ◽  
pp. 34-35
Author(s):  
J.R. McIntosh ◽  
D.L. Stemple ◽  
William Bishop ◽  
G.W. Hannaway
Keyword(s):  
Computer Graphics ◽  
Analytical Methods ◽  
Photographic Film ◽  
Complex Structures ◽  
Multiple Objects ◽  
Multiple Images ◽  
3 Dimensional

EM specimens often contain 3-dimensional information that is lost during micrography on a single photographic film. Two images of one specimen at appropriate orientations give a stereo view, but complex structures composed of multiple objects of graded density that superimpose in each projection are often difficult to decipher in stereo. Several analytical methods for 3-D reconstruction from multiple images of a serially tilted specimen are available, but they are all time-consuming and computationally intense.

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