Perspectives in Riemannian Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Perspectives in Riemannian Geometry write by Vestislav Apostolov. This book was released on 2006. Perspectives in Riemannian Geometry available in PDF, EPUB and Kindle. Special geometries as well as the relation between curvature and topology have always been of interest to differential geometers. More recently, these topics have turned out to be of use in physical problems related to string theory as well. This volume provides a unique and thorough survey on the latest developments on Riemannian geometry, special geometrical structures on manifolds, and their interactions with other fields such as mathematical physics, complex analysis, andalgebraic geometry. This volume presents ten papers written by participants of the ``Short Program on Riemannian Geometry,'' a workshop held at the CRM in Montreal in 2004. It will be a valuable reference for graduate students and research mathematicians alike. Information for our distributors: Titles inthis series are copublished with the Centre de Recherches Mathematiques.
On the Hypotheses Which Lie at the Bases of Geometry
On the Hypotheses Which Lie at the Bases of Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On the Hypotheses Which Lie at the Bases of Geometry write by Bernhard Riemann. This book was released on 2016-04-19. On the Hypotheses Which Lie at the Bases of Geometry available in PDF, EPUB and Kindle. This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary. The basic concepts and ideas, as well as their mathematical background, are provided, putting Riemann’s reasoning into the more general and systematic perspective achieved by later mathematicians and physicists (including Helmholtz, Ricci, Weyl, and Einstein) on the basis of his seminal ideas. Following a historical introduction that positions Riemann’s work in the context of his times, the history of the concept of space in philosophy, physics and mathematics is systematically presented. A subsequent chapter on the reception and influence of the text accompanies the reader from Riemann’s times to contemporary research. Not only mathematicians and historians of the mathematical sciences, but also readers from other disciplines or those with an interest in physics or philosophy will find this work both appealing and insightful.
Differential Geometry and Lie Groups
Differential Geometry and Lie Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry and Lie Groups write by Jean Gallier. This book was released on 2020-08-14. Differential Geometry and Lie Groups available in PDF, EPUB and Kindle. This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind many modern applications. Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry. Chapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.
Geometric Control Theory
Geometric Control Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Control Theory write by Velimir Jurdjevic. This book was released on 1997. Geometric Control Theory available in PDF, EPUB and Kindle. Geometric control theory is concerned with the evolution of systems subject to physical laws but having some degree of freedom through which motion is to be controlled. This book describes the mathematical theory inspired by the irreversible nature of time evolving events. The first part of the book deals with the issue of being able to steer the system from any point of departure to any desired destination. The second part deals with optimal control, the question of finding the best possible course. An overlap with mathematical physics is demonstrated by the Maximum principle, a fundamental principle of optimality arising from geometric control, which is applied to time-evolving systems governed by physics as well as to man-made systems governed by controls. Applications are drawn from geometry, mechanics, and control of dynamical systems. The geometric language in which the results are expressed allows clear visual interpretations and makes the book accessible to physicists and engineers as well as to mathematicians.
Sub-Riemannian Geometry and Optimal Transport
Sub-Riemannian Geometry and Optimal Transport - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sub-Riemannian Geometry and Optimal Transport write by Ludovic Rifford. This book was released on 2014-04-03. Sub-Riemannian Geometry and Optimal Transport available in PDF, EPUB and Kindle. The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is completely self-contained: the linear discussion, containing all the proofs of the stated results, leads the reader step by step from the notion of distribution at the very beginning to the existence of optimal transport maps for Lipschitz sub-Riemannian structure. The combination of geometry presented from an analytic point of view and of optimal transport, makes the book interesting for a very large community. This set of notes grew from a series of lectures given by the author during a CIMPA school in Beirut, Lebanon.
