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Quaternionic Contact


Quaternionic Contact
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Quaternionic Contact Einstein Structures And The Quaternionic Contact Yamabe Problem


Quaternionic Contact Einstein Structures And The Quaternionic Contact Yamabe Problem
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Author : A. L. Carey
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-08-12

Quaternionic Contact Einstein Structures And The Quaternionic Contact Yamabe Problem written by A. L. Carey and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-12 with Mathematics categories.


A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given. It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds. All conformal transformations sending the standard flat torsion-free quaternionic contact structure on the quaternionic Heisenberg group to a quaternionic contact structure with vanishing torsion of the Biquard connection are explicitly described. A "3-Hamiltonian form" of infinitesimal conformal automorphisms of quaternionic contact structures is presented.



Quaternionic Structures In Mathematics And Physics Proceedings Of The Second Meeting


Quaternionic Structures In Mathematics And Physics Proceedings Of The Second Meeting
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Author : Stefano Marchiafava
language : en
Publisher: World Scientific
Release Date : 2001-07-11

Quaternionic Structures In Mathematics And Physics Proceedings Of The Second Meeting written by Stefano Marchiafava and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-11 with Mathematics categories.


During the last five years, after the first meeting on “Quaternionic Structures in Mathematics and Physics”, interest in quaternionic geometry and its applications has continued to increase. Progress has been made in constructing new classes of manifolds with quaternionic structures (quaternionic Kähler, hyper-Kähler, hyper-complex, etc.), studying the differential geometry of special classes of such manifolds and their submanifolds, understanding relations between the quaternionic structure and other differential-geometric structures, and also in physical applications of quaternionic geometry. Some generalizations of classical quaternion-like structures (like HKT structures and hyper-Kähler manifolds with singularities) appeared naturally and were studied. Some of those results are published in this book.



Asymptotically Symmetric Einstein Metrics


Asymptotically Symmetric Einstein Metrics
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Author : Olivier Biquard
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Asymptotically Symmetric Einstein Metrics written by Olivier Biquard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.


The correspondence between Einstein metrics and their conformal boundaries has recently been the focus of great interest. This is particularly so in view of the relation with the physical theory of the AdS/CFT correspondence. In this book, this correspondence is seen in the wider context of asymptotically symmetric Einstein metrics, that is Einstein metrics whose curvature is asymptotic to that of a rank one symmetric space. There is an emphasis on the correspondence between Einstein metrics and geometric structures on their boundary at infinity: conformal structures, CR structures, and quaternionic contact structures introduced and studied in the book. Two new constructions of such Einstein metrics are given, using two different kinds of techniques: analytic methods to construct complete Einstein metrics, with a unified treatment of all rank one symmetric spaces, relying on harmonic analysis; algebraic methods (twistor theory) to construct local solutions of the Einstein equation near the boundary.



Current Developments In Differential Geometry And Its Related Fields Proceedings Of The 4th International Colloquium On Differential Geometry And Its Related Fields


Current Developments In Differential Geometry And Its Related Fields Proceedings Of The 4th International Colloquium On Differential Geometry And Its Related Fields
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Author : Toshiaki Adachi
language : en
Publisher: World Scientific
Release Date : 2015-10-22

Current Developments In Differential Geometry And Its Related Fields Proceedings Of The 4th International Colloquium On Differential Geometry And Its Related Fields written by Toshiaki Adachi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-22 with Mathematics categories.


This volume contains contributions by the main participants of the 4th International Colloquium on Differential Geometry and its Related Fields (ICDG2014). These articles cover recent developments and are devoted mainly to the study of some geometric structures on manifolds and graphs. Readers will find a broad overview of differential geometry and its relationship to other fields in mathematics and physics.



Parabolic Geometries I


Parabolic Geometries I
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Author : Andreas Čap
language : en
Publisher: American Mathematical Society
Release Date : 2024-07-29

Parabolic Geometries I written by Andreas Čap and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-29 with Mathematics categories.


Parabolic geometries encompass a very diverse class of geometric structures, including such important examples as conformal, projective, and almost quaternionic structures, hypersurface type CR-structures and various types of generic distributions. The characteristic feature of parabolic geometries is an equivalent description by a Cartan geometry modeled on a generalized flag manifold (the quotient of a semisimple Lie group by a parabolic subgroup). Background on differential geometry, with a view towards Cartan connections, and on semisimple Lie algebras and their representations, which play a crucial role in the theory, is collected in two introductory chapters. The main part discusses the equivalence between Cartan connections and underlying structures, including a complete proof of Kostant's version of the Bott–Borel–Weil theorem, which is used as an important tool. For many examples, the complete description of the geometry and its basic invariants is worked out in detail. The constructions of correspondence spaces and twistor spaces and analogs of the Fefferman construction are presented both in general and in several examples. The last chapter studies Weyl structures, which provide classes of distinguished connections as well as an equivalent description of the Cartan connection in terms of data associated to the underlying geometry. Several applications are discussed throughout the text.



Issues In General And Specialized Mathematics Research 2011 Edition


Issues In General And Specialized Mathematics Research 2011 Edition
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Author :
language : en
Publisher: ScholarlyEditions
Release Date : 2012-01-09

Issues In General And Specialized Mathematics Research 2011 Edition written by and has been published by ScholarlyEditions this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-09 with Mathematics categories.


Issues in General and Specialized Mathematics Research: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about General and Specialized Mathematics Research. The editors have built Issues in General and Specialized Mathematics Research: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General and Specialized Mathematics Research in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.



Hokkaido Mathematical Journal


Hokkaido Mathematical Journal
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Author :
language : en
Publisher:
Release Date : 2013

Hokkaido Mathematical Journal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.




Quaternionic Contact


Quaternionic Contact
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Author : Stefan P. Ivanov
language : en
Publisher:
Release Date : 2014

Quaternionic Contact written by Stefan P. Ivanov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Contact manifolds categories.


"Volume 231, number 1086 (third of 5 numbers), September 2014."



The Grothendieck Inequality Revisited


The Grothendieck Inequality Revisited
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Author : Ron Blei
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-09-29

The Grothendieck Inequality Revisited written by Ron Blei and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-29 with Mathematics categories.


The classical Grothendieck inequality is viewed as a statement about representations of functions of two variables over discrete domains by integrals of two-fold products of functions of one variable. An analogous statement is proved, concerning continuous functions of two variables over general topological domains. The main result is the construction of a continuous map $\Phi$ from $l^2(A)$ into $L^2(\Omega_A, \mathbb{P}_A)$, where $A$ is a set, $\Omega_A = \{-1,1\}^A$, and $\mathbb{P}_A$ is the uniform probability measure on $\Omega_A$.



Local Entropy Theory Of A Random Dynamical System


Local Entropy Theory Of A Random Dynamical System
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Author : Anthony H. Dooley
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20

Local Entropy Theory Of A Random Dynamical System written by Anthony H. Dooley and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.


In this paper the authors extend the notion of a continuous bundle random dynamical system to the setting where the action of R or N is replaced by the action of an infinite countable discrete amenable group. Given such a system, and a monotone sub-additive invariant family of random continuous functions, they introduce the concept of local fiber topological pressure and establish an associated variational principle, relating it to measure-theoretic entropy. They also discuss some variants of this variational principle. The authors introduce both topological and measure-theoretic entropy tuples for continuous bundle random dynamical systems, and apply variational principles to obtain a relationship between these of entropy tuples. Finally, they give applications of these results to general topological dynamical systems, recovering and extending many recent results in local entropy theory.