Modern Geometric Structures and Fields

Modern Geometric Structures and Fields

Author: Сергей Петрович Новиков

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 658

ISBN-13: 0821839292

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Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.


An Anthology of Structural Morphology

An Anthology of Structural Morphology

Author: Rene Motro

Publisher: World Scientific

Published: 2009

Total Pages: 211

ISBN-13: 9812837213

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The structural morphology working group of the International Association for Shell and Spatial Structures, founded in 1991, has helped to launch several international seminars, newsletters and specific sessions of international conferences devoted to structural morphology. This book contains papers that have been selected either for their fundamental contribution to structural morphology or for their actual pertinence in the field. Polyhedral geometry, double-curved surfaces, biological structures, foldable systems, form-finding techniques, and free form design are some of the topics included in the contents of this book. The work presented in this book is the result of more than 15 years of study by researchers, engineers, mathematicians, and architects, who thought that conceptual design would benefit from the association of separate fields (geometry, biology, and mechanics) in a holistic process. Every aspect of structural morphology is illustrated by one or more chapters of the book. As far as we know, there are few books OCo perhaps none OCo that gather all aspects of structural morphology, even if, for instance, there are many books on the geometry of polyhedra. Furthermore, readers will have access to a large list of selected references, which will open the scope of their bibliography. Sample Chapter(s). Chapter 1: The First 13 Years of Structural Morphology Group OCo A Personal View (2,623 KB). Contents: The First 13 Years of Structural Morphology Group OCo A Personal View (T Wester); An Approach to Structural Morphology (R Motro); The Structural Morphology of Curved Diaphragms OCo Or the Structural Behavior of Floral Polyhedra (T Wester); Polyhedroids (P Huybers); Novational Transformations (H Nooshin et al.); Some Structural-Morphological Aspects of Deployable Structures for Space Enclosures (A Hanaor); Phantasy in Space: On Human Feeling Between the Shapes of the World and How to Look on Natural Structures (M Balz); An Expandable Dodecahedron (K Flriin & T Tabor); Examples of Geometrical Reverse Engineering: Designing from Models and/or Under Geometrical Constraints (K Linkwitz); Crystalline Architecture (A L Loeb); Flat Grids Designs Employing the Swivel Diaphragm (C Rodriguez et al.); Form Optimizing in Biological Structures OCo The Morphology of Sea Shells (E Stach); Expandable OCyBlobOCO Structures (F Jensen & S Pellegrino). Readership: Advanced undergraduates and graduate students in mechanics, civil engineering, architecture and design; architects; engineers."


Advanced Structural Safety Studies

Advanced Structural Safety Studies

Author: Jeom Kee Paik

Publisher: Springer

Published: 2019-07-25

Total Pages: 682

ISBN-13: 981138245X

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This book describes principles, industry practices and evolutionary methodologies for advanced safety studies, which are helpful in effectively managing volatile, uncertain, complex, and ambiguous (VUCA) environments within the framework of quantitative risk assessment and management and associated with the safety and resilience of structures and infrastructures with tolerance against various types of extreme conditions and accidents such as fires, explosions, collisions and grounding. It presents advanced computational models for characterizing structural actions and their effects in extreme and accidental conditions, which are highly nonlinear and non-Gaussian in association with multiple physical processes, multiple scales, and multiple criteria. Probabilistic scenario selection practices and applications are presented. Engineering practices for structural crashworthiness analysis in extreme conditions and accidents are described. Multidisciplinary approaches involving advanced computational models and large-scale physical model testing are emphasized. The book will be useful to students at a post-graduate level as well as researchers and practicing engineers.


Complex Geometry

Complex Geometry

Author: Daniel Huybrechts

Publisher: Springer Science & Business Media

Published: 2005

Total Pages: 336

ISBN-13: 9783540212904

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Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)


Hodge Theory and Complex Algebraic Geometry I:

Hodge Theory and Complex Algebraic Geometry I:

Author: Claire Voisin

Publisher: Cambridge University Press

Published: 2007-12-20

Total Pages: 334

ISBN-13: 9780521718011

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This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.


Riemannian Geometry

Riemannian Geometry

Author: Isaac Chavel

Publisher: Cambridge University Press

Published: 2006-04-10

Total Pages: 4

ISBN-13: 1139452576

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This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.