Rigidity And Symmetry
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Rigidity And Symmetry
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Author : Robert Connelly
language : en
Publisher: Springer
Release Date : 2014-06-11
Rigidity And Symmetry written by Robert Connelly and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-11 with Mathematics categories.
This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and combinatorics. Contributions present recent trends and advances in discrete geometry, particularly in the theory of polytopes. The rapid development of abstract polytope theory has resulted in a rich theory featuring an attractive interplay of methods and tools from discrete geometry, group theory, classical geometry, hyperbolic geometry and topology. Overall, the book shows how researchers from diverse backgrounds explore connections among the various discrete structures with symmetry as the unifying theme. The volume will be a valuable source as an introduction to the ideas of both combinatorial and geometric rigidity theory and its applications, incorporating the surprising impact of symmetry. It will appeal to students at both the advanced undergraduate and graduate levels, as well as post docs, structural engineers and chemists.
Strong Rigidity Of Locally Symmetric Spaces Am 78 Volume 78
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Author : G. Daniel Mostow
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Strong Rigidity Of Locally Symmetric Spaces Am 78 Volume 78 written by G. Daniel Mostow and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini, Weil, Borel, and Raghunathan. The proof combines the theory of semi-simple Lie groups, discrete subgroups, the geometry of E. Cartan's symmetric Riemannian spaces, elements of ergodic theory, and the fundamental theorem of projective geometry as applied to Tit's geometries. In his proof the author introduces two new notions having independent interest: one is "pseudo-isometries"; the other is a notion of a quasi-conformal mapping over the division algebra K (K equals real, complex, quaternion, or Cayley numbers). The author attempts to make the account accessible to readers with diverse backgrounds, and the book contains capsule descriptions of the various theories that enter the proof.
Metric Rigidity Theorems On Hermitian Locally Symmetric Manifolds
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Author : Ngaiming Mok
language : en
Publisher: World Scientific
Release Date : 1989
Metric Rigidity Theorems On Hermitian Locally Symmetric Manifolds written by Ngaiming Mok and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
This monograph studies the problem of characterizing canonical metrics on Hermitian locally symmetric manifolds X of non-compact/compact types in terms of curvature conditions. The proofs of these metric rigidity theorems are applied to the study of holomorphic mappings between manifolds X of the same type. Moreover, a dual version of the generalized Frankel Conjecture on characterizing compact Khler manifolds are also formulated.
Frameworks Tensegrities And Symmetry
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Author : Robert Connelly
language : en
Publisher: Cambridge University Press
Release Date : 2022-01-27
Frameworks Tensegrities And Symmetry written by Robert Connelly and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-27 with Mathematics categories.
Why don't things fall down? Engineering meets mathematics in this introduction to the geometry of rigid and flexible structures.
Geometry Rigidity And Group Actions
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Author : Robert J Zimmer
language : en
Publisher: University of Chicago Press
Release Date : 2011-04-15
Geometry Rigidity And Group Actions written by Robert J Zimmer and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-15 with Mathematics categories.
The study of group actions is more than a hundred years old but remains to this day a vibrant and widely studied topic in a variety of mathematic fields. A central development in the last fifty years is the phenomenon of rigidity, whereby one can classify actions of certain groups, such as lattices in semi-simple Lie groups. This provides a way to classify all possible symmetries of important spaces and all spaces admitting given symmetries. Paradigmatic results can be found in the seminal work of George Mostow, Gergory Margulis, and Robert J. Zimmer, among others. The papers in Geometry, Rigidity, and Group Actions explore the role of group actions and rigidity in several areas of mathematics, including ergodic theory, dynamics, geometry, topology, and the algebraic properties of representation varieties. In some cases, the dynamics of the possible group actions are the principal focus of inquiry. In other cases, the dynamics of group actions are a tool for proving theorems about algebra, geometry, or topology. This volume contains surveys of some of the main directions in the field, as well as research articles on topics of current interest.
Handbook Of Geometric Constraint Systems Principles
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Author : Meera Sitharam
language : en
Publisher: CRC Press
Release Date : 2018-07-20
Handbook Of Geometric Constraint Systems Principles written by Meera Sitharam and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-20 with Mathematics categories.
The Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. Key Features: A comprehensive reference handbook authored by top researchers Includes fundamentals and techniques from multiple perspectives that span several research communities Provides recent results and a graded program of open problems and conjectures Can be used for senior undergraduate or graduate topics course introduction to the area Detailed list of figures and tables About the Editors: Meera Sitharam is currently an Associate Professor at the University of Florida’s Department of Computer & Information Science and Engineering. She received her Ph.D. at the University of Wisconsin, Madison. Audrey St. John is an Associate Professor of Computer Science at Mount Holyoke College, who received her Ph. D. from UMass Amherst. Jessica Sidman is a Professor of Mathematics on the John S. Kennedy Foundation at Mount Holyoke College. She received her Ph.D. from the University of Michigan.
Frameworks Tensegrities And Symmetry
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Author : Robert Connelly
language : en
Publisher: Cambridge University Press
Release Date : 2022-01-27
Frameworks Tensegrities And Symmetry written by Robert Connelly and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-27 with Mathematics categories.
This introduction to the theory of rigid structures explains how to analyze the performance of built and natural structures under loads, paying special attention to the role of geometry. The book unifies the engineering and mathematical literatures by exploring different notions of rigidity - local, global, and universal - and how they are interrelated. Important results are stated formally, but also clarified with a wide range of revealing examples. An important generalization is to tensegrities, where fixed distances are replaced with 'cables' not allowed to increase in length and 'struts' not allowed to decrease in length. A special feature is the analysis of symmetric tensegrities, where the symmetry of the structure is used to simplify matters and allows the theory of group representations to be applied. Written for researchers and graduate students in structural engineering and mathematics, this work is also of interest to computer scientists and physicists.
Symmetry As A Developmental Principle In Nature And Art
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Author : Werner Hahn
language : en
Publisher: World Scientific
Release Date : 1998
Symmetry As A Developmental Principle In Nature And Art written by Werner Hahn and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
Looking beyond the boundaries of various disciplines, the author demonstrates that symmetry is a fascinating phenomenon which provides endless stimulation and challenges. He explains that it is possible to readapt art to the sciences, and vice versa, by means of an evolutionary concept of symmetry. Many pictorial examples are included to enable the reader to fully understand the issues discussed. Based on the artistic evidence that the author has collected, he proposes that the new ars evolutoria can function as an example for the sciences.The book is divided into three distinct parts, each one focusing on a special issue. In Part I, the phenomenon of symmetry, including its discovery and meaning is reviewed. The author looks closely at how Vitruvius, Polyclitus, Democritus, Plato, Aristotle, Plotinus, Augustine, Alberti, Leonardo da Vinci and Durer viewed symmetry. This is followed by an explanation on how the concept of symmetry developed. The author further discusses symmetry as it appears in art and science, as well as in the modern age. Later, he expounds the view of symmetry as an evolutionary concept which can lead to a new unity of science. In Part II, he covers the points of contact between the form-developing process in nature and art. He deals with biological questions, in particular evolution.The collection of new and precise data on perception and knowledge with regard to the postulated reality of symmetry leads to further development of the evolutionary theory of symmetry in Part III. The author traces the enormous treasure of observations made in nature and culture back to a few underlying structural principles. He demonstrates symmetry as a far-reaching, leading, structuring, causal element of evolution, as the idea lying behind nature and culture. Numerous controllable reproducible double-mirror experiments on a new stereoscopic vision verify a symmetrization theory of perception.
Rigidity And Quasi Rigidity Of Extremal Cycles In Hermitian Symmetric Spaces Am 153
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Author : Robert L. Bryant
language : en
Publisher:
Release Date : 2010
Rigidity And Quasi Rigidity Of Extremal Cycles In Hermitian Symmetric Spaces Am 153 written by Robert L. Bryant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This book investigates the geometry of complex subvarieties of compact Hermitian symmetric spaces, particularly the complex Grassmannians, which are central to Schubert calculus and its applications to enumerative algebraic geometry. To do so, Robert Bryant employs a combination of Hermitian differential geometry, calibrations, and classical moving frame constructions. The main result is that, for Hermitian symmetric spaces M of rank greater than 1, there are homology classes c (called extremal) such that the complex varieties V in M that represent c display rigidity in unexpected ways. There are other cycles that display a weaker form of this sort of rigidity, but whose moduli space of representing cycles can still be described in terms of the geometry of subvarieties of related complex projective spaces. These results have applications to other problems in algebraic geometry. For example, for a holomorphic bundle E over a compact complex manifold M that is generated by its sections, the Schur polynomials in its Chern classes are known to be non-negative. The above results allow one to give a complete description of such bundles in several cases where one of these Schur polynomials actually vanishes. The book, which will interest researchers and graduate students in complex algebraic geometry or differential geometry, contains a thorough exposition of the geometry of Hermitian symmetric spaces and their Schubert cycles and characteristic classes as well as other preparatory material needed to obtain the results.
Handbook Of Discrete And Computational Geometry
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Author : Csaba D. Toth
language : en
Publisher: CRC Press
Release Date : 2017-11-22
Handbook Of Discrete And Computational Geometry written by Csaba D. Toth and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Computers categories.
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.