scholarly journals Geometry of nilmanifolds with left-invariant complex structure and deformations in the large

2009 ◽  
Vol 99 (2) ◽  
pp. 425-460 ◽  
Author(s):  
Sönke Rollenske
Keyword(s):  
Complex Structure ◽  
Invariant Complex Structure

scholarly journals On the Bott–Chern cohomology and balanced Hermitian nilmanifolds

2014 ◽  
Vol 25 (06) ◽  
pp. 1450057 ◽  
Author(s):  
Adela Latorre ◽  
Luis Ugarte ◽  
Raquel Villacampa
Keyword(s):  
Cohomology Group ◽  
Complex Structure ◽  
Hermitian Metrics ◽  
Invariant Complex Structure

The Bott–Chern cohomology of six-dimensional nilmanifolds endowed with invariant complex structure is studied with special attention to the cases when balanced or strongly Gauduchon Hermitian metrics exist. We consider complex invariants introduced by Angella and Tomassini and by Schweitzer, which are related to the [Formula: see text]-lemma condition and defined in terms of the Bott–Chern cohomology, and show that the vanishing of some of these invariants is not a closed property under holomorphic deformations. In the balanced case, we determine the spaces that parametrize deformations in type IIB supergravity described by Tseng and Yau in terms of the Bott–Chern cohomology group of bidegree (2, 2).

scholarly journals STABILITY OF ABELIAN COMPLEX STRUCTURES

2006 ◽  
Vol 17 (04) ◽  
pp. 401-416 ◽  
Author(s):  
S. CONSOLE ◽  
A. FINO ◽  
Y. S. POON
Keyword(s):  
Deformation Process ◽  
Complex Structure ◽  
Complex Structures ◽  
Higher Dimension ◽  
Real Dimension ◽  
Small Deformations ◽  
Invariant Complex Structure

Let M = Γ\G be a nilmanifold endowed with an invariant complex structure. We prove that Kuranishi deformations of abelian complex structures are all invariant complex structures, generalizing a result in [7] for 2-step nilmanifolds. We characterize small deformations that remain abelian. As an application, we observe that at real dimension six, the deformation process of abelian complex structures is stable within the class of nilpotent complex structures. We give an example to show that this property does not hold in higher dimension.

On the Kobayashi Pseudometric Reduction of Homogeneous Spaces

1988 ◽  
Vol 31 (1) ◽  
pp. 45-51 ◽  
Author(s):  
Bruce Gilligan
Keyword(s):  
Bounded Domain ◽  
Complex Manifold ◽  
Homogeneous Spaces ◽  
Complex Structure ◽  
Complex Submanifold ◽  
Technical Assumption ◽  
Homogeneous Complex ◽  
Homogeneous Complex Manifold ◽  
Kobayashi Pseudometric ◽  
Invariant Complex Structure

AbstractGiven any homogeneous complex manifold X = G/H, there exists a natural coset map π :G/H → G/K satisfying π (X1) = π (x2) if and only if dx(x1 x2) = 0, where dx denotes the Kobayashi pseudometric on X. Its typical fiber Z : = K/H is a connected complex submanifold of X. Also G/K has a (7-invariant complex structure, provided K satisfies a certain technical assumption (see Theorem 3). If Z is compact as well, then G/K is biholomorphic to a homogeneous bounded domain.

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.

COMPLEX STRUCTURES ON FOUR-MANIFOLDS WITH SYMPLECTIC TWO-TORUS ACTIONS

2011 ◽  
Vol 22 (03) ◽  
pp. 449-463 ◽  
Author(s):  
J. J. DUISTERMAAT ◽  
A. PELAYO
Keyword(s):  
General Theory ◽  
Complex Structure ◽  
Torus Action ◽  
K3 Surface ◽  
Complex Structures ◽  
Complex Surfaces ◽  
Torus Actions ◽  
Kähler Structure ◽  
Four Manifolds ◽  
Invariant Complex Structure

We apply the general theory for symplectic torus actions with symplectic or coisotropic orbits to prove that a four-manifold with a symplectic two-torus action admits an invariant complex structure and give an identification of those that do not admit a Kähler structure with Kodaira's class of complex surfaces which admit a nowhere vanishing holomorphic (2,0)-form, but are not a torus nor a K3 surface.

A new method of complex structure analysis by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 628-629
Author(s):  
V.V. Rybin ◽  
E.V. Voronina
Keyword(s):  
Complex Structure ◽  
Reciprocal Lattice ◽  
Stacking Faults ◽  
Plastic Strains ◽  
Base Position ◽  
Structural Regularity ◽  
Orientation Matrix ◽  
Computerized Processing ◽  
Fully Automatic ◽  
Diffraction Patterns

Recently, it has become essential to develop a helpful method of the complete crystallographic identification of fine fragmented crystals. This was maainly due to the investigation into structural regularity of large plastic strains. The method should be practicable for determining crystallographic orientation (CO) of elastically stressed micro areas of the order of several micron fractions in size and filled with λ>1010 cm-2 density dislocations or stacking faults. The method must provide the misorientation vectors of the adjacent fragments when the angle ω changes from 0 to 180° with the accuracy of 0,3°. The problem is that the actual electron diffraction patterns obtained from fine fragmented crystals are the superpositions of reflections from various fragments, though more than one or two reflections from a fragment are hardly possible. Finally, the method should afford fully automatic computerized processing of the experimental results.The proposed method meets all the above requirements. It implies the construction for a certain base position of the crystal the orientation matrix (0M) A, which gives a single intercorrelation between the coordinates of the unity vector in the reference coordinate system (RCS) and those of the same vector in the crystal reciprocal lattice base : .

Computer processing of high-resolution images of periodic specimens

1986 ◽  
Vol 44 ◽  
pp. 2-5
Author(s):  
W. Chiu ◽  
M.F. Schmid ◽  
T.-W. Jeng
Keyword(s):  
High Resolution ◽  
Fourier Transforms ◽  
Complex Structure ◽  
Distribution Functions ◽  
Multiple Image ◽  
Cryo Electron Microscopy ◽  
Structure Factors ◽  
Unit Cells ◽  
High Resolution Images ◽  
Phase Probability Distribution

Cryo-electron microscopy has been developed to the point where one can image thin protein crystals to 3.5 Å resolution. In our study of the crotoxin complex crystal, we can confirm this structural resolution from optical diffractograms of the low dose images. To retrieve high resolution phases from images, we have to include as many unit cells as possible in order to detect the weak signals in the Fourier transforms of the image. Hayward and Stroud proposed to superimpose multiple image areas by combining phase probability distribution functions for each reflection. The reliability of their phase determination was evaluated in terms of a crystallographic “figure of merit”. Grant and co-workers used a different procedure to enhance the signals from multiple image areas by vector summation of the complex structure factors in reciprocal space.

A large rotating structure around AB Doradus A at VLBI scale

2019 ◽  
Vol 15 (S354) ◽  
pp. 189-194
Author(s):  
J. B. Climent ◽  
J. C. Guirado ◽  
R. Azulay ◽  
J. M. Marcaide
Keyword(s):  
Magnetic Reconnection ◽  
Main Sequence ◽  
Complex Structure ◽  
Main Sequence Star ◽  
Polar Cap ◽  
Vlbi Observations ◽  
Rotating Structure ◽  
Source Structure ◽  
Expected Position

AbstractWe report the results of three VLBI observations of the pre-main-sequence star AB Doradus A at 8.4 GHz. With almost three years between consecutive observations, we found a complex structure at the expected position of this star for all epochs. Maps at epochs 2007 and 2010 show a double core-halo morphology while the 2013 map reveals three emission peaks with separations between 5 and 18 stellar radii. Furthermore, all maps show a clear variation of the source structure within the observing time. We consider a number of hypothesis in order to explain such observations, mainly: magnetic reconnection in loops on the polar cap, a more general loop scenario and a close companion to AB Dor A.

SAC3B is a target of CML19, the centrin 2 of Arabidopsis thaliana

2020 ◽  
Vol 477 (1) ◽  
pp. 173-189 ◽  
Author(s):  
Marco Pedretti ◽  
Carolina Conter ◽  
Paola Dominici ◽  
Alessandra Astegno
Keyword(s):  
Excision Repair ◽  
Complex Structure ◽  
Binding Motif ◽  
C Terminus ◽  
Repair Protein ◽  
Nucleotide Excision ◽  
Ef Hand ◽  
Molecular Determinants ◽  
Structure In Solution

Arabidopsis centrin 2, also known as calmodulin-like protein 19 (CML19), is a member of the EF-hand superfamily of calcium (Ca2+)-binding proteins. In addition to the notion that CML19 interacts with the nucleotide excision repair protein RAD4, CML19 was suggested to be a component of the transcription export complex 2 (TREX-2) by interacting with SAC3B. However, the molecular determinants of this interaction have remained largely unknown. Herein, we identified a CML19-binding site within the C-terminus of SAC3B and characterized the binding properties of the corresponding 26-residue peptide (SAC3Bp), which exhibits the hydrophobic triad centrin-binding motif in a reversed orientation (I8W4W1). Using a combination of spectroscopic and calorimetric experiments, we shed light on the SAC3Bp–CML19 complex structure in solution. We demonstrated that the peptide interacts not only with Ca2+-saturated CML19, but also with apo-CML19 to form a protein–peptide complex with a 1 : 1 stoichiometry. Both interactions involve hydrophobic and electrostatic contributions and include the burial of Trp residues of SAC3Bp. However, the peptide likely assumes different conformations upon binding to apo-CML19 or Ca2+-CML19. Importantly, the peptide dramatically increases the affinity for Ca2+ of CML19, especially of the C-lobe, suggesting that in vivo the protein would be Ca2+-saturated and bound to SAC3B even at resting Ca2+-levels. Our results, providing direct evidence that Arabidopsis SAC3B is a CML19 target and proposing that CML19 can bind to SAC3B through its C-lobe independent of a Ca2+ stimulus, support a functional role for these proteins in TREX-2 complex and mRNA export.

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