scholarly journals Local Models of Isolated Singularities for Affine Special Kähler Structures in Dimension Two

2018 ◽  
Vol 2020 (17) ◽  
pp. 5215-5235 ◽  
Author(s):  
Martin Callies ◽  
Andriy Haydys
Keyword(s):  
Local Models ◽  
Isolated Singularities ◽  
Kähler Structure ◽  
Real Dimension ◽  
Cubic Form ◽  
Kähler Structures ◽  
Symplectic Connection

Abstract We construct local models of isolated singularities for special Kähler structures in real dimension two assuming that the associated holomorphic cubic form does not have essential singularities. As an application we compute the holonomy of the flat symplectic connection, which is a part of the special Kähler structure.

scholarly journals A note about invariant SKT structures and generalized Kähler structures on flag manifolds

2012 ◽  
Vol 55 (3) ◽  
pp. 543-549 ◽  
Author(s):  
Dmitri V. Alekseevsky ◽  
Liana David
Keyword(s):  
Lie Group ◽  
Flag Manifold ◽  
Flag Manifolds ◽  
Compact Lie Group ◽  
Kähler Structure ◽  
Kähler Structures

AbstractWe prove that any invariant strong Kähler structure with torsion (SKT structure) on a flag manifold M = G/K of a semi-simple compact Lie group G is Kähler. As an application we describe invariant generalized Kähler structures on M.

scholarly journals Symplectic and Kähler structures on $$\mathbb CP^1$$-bundles over $$\mathbb CP^2$$

2021 ◽  
Vol 27 (5) ◽  
Author(s):  
Nicholas Lindsay ◽  
Dmitri Panov
Keyword(s):  
Vector Bundles ◽  
Symplectic Structures ◽  
Kähler Structure ◽  
Mori Theory ◽  
Holomorphic Vector Bundles ◽  
Kähler Structures

AbstractWe show that there exist symplectic structures on a $$\mathbb {CP}^1$$ CP 1 -bundle over $$\mathbb {CP}^2$$ CP 2 that do not admit a compatible Kähler structure. These symplectic structures were originally constructed by Tolman and they have a Hamiltonian $${\mathbb {T}}^2$$ T 2 -symmetry. Tolman’s manifold was shown to be diffeomorphic to a $$\mathbb CP^1$$ C P 1 -bundle over $$\mathbb {CP}^{2}$$ CP 2 by Goertsches, Konstantis, and Zoller. The proof of our result relies on Mori theory, and on classical facts about holomorphic vector bundles over $$\mathbb {CP}^{2}$$ CP 2 .

scholarly journals Generalized Kähler Metrics from Hamiltonian Deformations

2018 ◽  
pp. 551-580
Author(s):  
Marco Gualtieri
Keyword(s):  
The Other ◽  
Alternative Proof ◽  
Poisson Structures ◽  
Kähler Metrics ◽  
Kähler Structure ◽  
Dirac Structures ◽  
Main Application ◽  
Close Relationship ◽  
Kähler Structures

This chapter provides a new characterization of generalized Kähler structures in terms of the corresponding complex Dirac structures. It then gives an alternative proof of Hitchin’s partial unobstructedness for holomorphic Poisson structures. Its main application is to show that there is a corresponding unobstructedness result for arbitrary generalized Kähler structures. That is, it shows that any generalized Kähler structure may be deformed in such a way that one of its underlying holomorphic Poisson structures remains fixed, while the other deforms via Hitchin’s deformation. Finally, it indicates a close relationship between this deformation and the notion of a Hamiltonian family of Poisson structures.

Structures of chemically stabilized ceramics

1993 ◽  
Vol 51 ◽  
pp. 924-925
Author(s):  
Pratibha L. Gai ◽  
M. A. Saltzberg ◽  
L.G. Hanna ◽  
S.C. Winchester
Keyword(s):  
High Temperature ◽  
Calcium Nitrate ◽  
Nitrate Hexahydrate ◽  
Chemical Route ◽  
Cubic Form ◽  
Tetragonal Form ◽  
Wet Chemical ◽  
Wet Chemical Route ◽  
Final Composition ◽  
Aluminium Nitrate Nonahydrate

Silica based ceramics are some of the most fundamental in crystal chemistry. The cristobalite form of silica has two modifications, α (low temperature, tetragonal form) and β (high temperature, cubic form). This paper describes our structural studies of unusual chemically stabilized cristobalite (CSC) material, a room temperature silica-based ceramic containing small amounts of dopants, prepared by a wet chemical route. It displays many of the structural charatcteristics of the high temperature β-cristobalite (∼270°C), but does not undergo phase inversion to α-cristobalite upon cooling. The Structure of α-cristobalite is well established, but that of β is not yet fully understood.Compositions with varying Ca/Al ratio and substitutions in cristobalite were prepared in the series, CaO:Al2O3:SiO2 : 3-x: x : 40, with x= 0-3. For CSC, a clear sol was prepared from Du Pont colloidal silica, Ludox AS-40®, aluminium nitrate nonahydrate, and calcium nitrate hexahydrate in proportions to form a final composition 1:2:40 composition.

Kisin modules with descent data and parahoric local models

2018 ◽  
Vol 51 (1) ◽  
pp. 181-213 ◽  
Author(s):  
Ana Caraiani ◽  
Brandon Levin
Keyword(s):  
Local Models ◽  
Descent Data

Spheric radial basis functions in Mahalanobis measuring for displaying local field features

2019 ◽  
Vol 952 (10) ◽  
pp. 2-9
Author(s):  
Yu.M. Neiman ◽  
L.S. Sugaipova ◽  
V.V. Popadyev
Keyword(s):  
Gravitational Field ◽  
Quadratic Form ◽  
Local Field ◽  
Euclidean Distance ◽  
Basis Functions ◽  
Spherical Functions ◽  
Local Models ◽  
Stationary Field ◽  
Modeling Process ◽  
The Earth

As we know the spherical functions are traditionally used in geodesy for modeling the gravitational field of the Earth. But the gravitational field is not stationary either in space or in time (but the latter is beyond the scope of this article) and can change quite strongly in various directions. By its nature, the spherical functions do not fully display the local features of the field. With this in mind it is advisable to use spatially localized basis functions. So it is convenient to divide the region under consideration into segments with a nearly stationary field. The complexity of the field in each segment can be characterized by means of an anisotropic matrix resulting from the covariance analysis of the field. If we approach the modeling in this way there can arise a problem of poor coherence of local models on segments’ borders. To solve the above mentioned problem it is proposed in this article to use new basis functions with Mahalanobis metric instead of the usual Euclidean distance. The Mahalanobis metric and the quadratic form generalizing this metric enables us to take into account the structure of the field when determining the distance between the points and to make the modeling process continuous.

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