Proceedings Of The Meeting On Quaternionic Structures In Mathematics And Physics
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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.
A New Construction Of Homogeneous Quaternionic Manifolds And Related Geometric Structures
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Author : Vicente Cortés
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
A New Construction Of Homogeneous Quaternionic Manifolds And Related Geometric Structures written by Vicente Cortés 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 2000 with Mathematics categories.
Let $V = {\mathbb R}^{p,q}$ be the pseudo-Euclidean vector space of signature $(p,q)$, $p\ge 3$ and $W$ a module over the even Clifford algebra $C\! \ell^0 (V)$. A homogeneous quaternionic manifold $(M,Q)$ is constructed for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \wedge^2 W \rightarrow V$. If the skew symmetric vector valued bilinear form $\Pi$ is nondegenerate then $(M,Q)$ is endowed with a canonical pseudo-Riemannian metric $g$ such that $(M,Q,g)$ is a homogeneous quaternionic pseudo-Kahler manifold. If the metric $g$ is positive definite, i.e. a Riemannian metric, then the quaternionic Kahler manifold $(M,Q,g)$ is shown to admit a simply transitive solvable group of automorphisms. In this special case ($p=3$) we recover all the known homogeneous quaternionic Kahler manifolds of negative scalar curvature (Alekseevsky spaces) in a unified and direct way. If $p>3$ then $M$ does not admit any transitive action of a solvable Lie group and we obtain new families of quaternionic pseudo-Kahler manifolds. Then it is shown that for $q = 0$ the noncompact quaternionic manifold $(M,Q)$ can be endowed with a Riemannian metric $h$ such that $(M,Q,h)$ is a homogeneous quaternionic Hermitian manifold, which does not admit any transitive solvable group of isometries if $p>3$. The twistor bundle $Z \rightarrow M$ and the canonical ${\mathrm SO}(3)$-principal bundle $S \rightarrow M$ associated to the quaternionic manifold $(M,Q)$ are shown to be homogeneous under the automorphism group of the base. More specifically, the twistor space is a homogeneous complex manifold carrying an invariant holomorphic distribution $\mathcal D$ of complex codimension one, which is a complex contact structure if and only if $\Pi$ is nondegenerate. Moreover, an equivariant open holomorphic immersion $Z \rightarrow \bar{Z}$ into a homogeneous complex manifold $\bar{Z}$ of complex algebraic group is constructed. Finally, the construction is shown to have a natural mirror in the category of supermanifolds. In fact, for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \vee^2 W \rightarrow V$ a homogeneous quaternionic supermanifold $(M,Q)$ is constructed and, moreover, a homogeneous quaternionic pseudo-Kahler supermanifold $(M,Q,g)$ if the symmetric vector valued bilinear form $\Pi$ is nondegenerate.
High Energy Physics And Cosmology Proceedings Of The 1995 Summer School
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Author : E Gava
language : en
Publisher: World Scientific
Release Date : 1997-02-27
High Energy Physics And Cosmology Proceedings Of The 1995 Summer School written by E Gava and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-27 with categories.
Poisson Structures And Their Normal Forms
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Author : Jean-Paul Dufour
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-17
Poisson Structures And Their Normal Forms written by Jean-Paul Dufour and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-17 with Mathematics categories.
The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.
Riemannian Submersions And Related Topics
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Author : Maria Falcitelli
language : en
Publisher: World Scientific
Release Date : 2004
Riemannian Submersions And Related Topics written by Maria Falcitelli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
- First systematic exposition devoted to Riemannian submersions - Deals with current material - Contains a wide-ranging bibliography and about 350 references
N 2 Supergravity In D 4 5 6 Dimensions
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Author : Edoardo Lauria
language : en
Publisher: Springer Nature
Release Date : 2020-03-11
N 2 Supergravity In D 4 5 6 Dimensions written by Edoardo Lauria and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-11 with Science categories.
This graduate-level primer presents a tutorial introduction to and overview of N = 2 supergravity theories - with 8 real supercharges and in 4, 5 and 6 dimensions. First, the construction of such theories by superconformal methods is explained in detail, and relevant special geometries are obtained and characterized. Following, the relation between the supergravity theories in the various dimensions is discussed. This leads eventually to the concept of very special geometry and quaternionic-Kähler manifolds. This concise text is a valuable resource for graduate students and young researchers wishing to enter the field quickly and efficiently.
Proceedings Of The Meeting On Quaternionic Structures In Mathematics And Physics
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Author : E. Bonan
language : en
Publisher:
Release Date : 1995
Proceedings Of The Meeting On Quaternionic Structures In Mathematics And Physics written by E. Bonan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Lectures On Hyperhamiltonian Dynamics And Physical Applications
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Author : Giuseppe Gaeta
language : en
Publisher: Springer
Release Date : 2017-07-21
Lectures On Hyperhamiltonian Dynamics And Physical Applications written by Giuseppe Gaeta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-21 with Science categories.
This book provides the mathematical foundations of the theory of hyperhamiltonian dynamics, together with a discussion of physical applications. In addition, some open problems are discussed. Hyperhamiltonian mechanics represents a generalization of Hamiltonian mechanics, in which the role of the symplectic structure is taken by a hyperkähler one (thus there are three Kähler/symplectic forms satisfying quaternionic relations). This has proved to be of use in the description of physical systems with spin, including those which do not admit a Hamiltonian formulation. The book is the first monograph on the subject, which has previously been treated only in research papers.
Supersymmetric Mechanics Vol 2
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Author : Stefano Bellucci
language : en
Publisher: Springer
Release Date : 2006-09-11
Supersymmetric Mechanics Vol 2 written by Stefano Bellucci and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-11 with Science categories.
This is the first volume in a series of books on the general theme of Supersymmetric Mechanics; the series is based on lectures and discussions held in 2005 and 2006 at the INFN-Laboratori Nazionali di Frascati. This volume supplies a pedagogical introduction, at the non-expert level, to the attractor mechanism in space-time singularities. After a qualitative overview, explicit examples realizing the attractor mechanism are treated at length.
Balkan Journal Of Geometry And Its Applications
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Author :
language : en
Publisher:
Release Date : 2004
Balkan Journal Of Geometry And Its Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Geometry categories.