differential geometric structures dover books on mathematics

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Differential Geometric Structures

Author : Walter A. Poor
ISBN : 9780486151915
Genre : Mathematics
File Size : 43. 69 MB
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This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.

Differential Geometry

Author : Erwin Kreyszig
ISBN : 0486667219
Genre : Mathematics
File Size : 82. 8 MB
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Text from preface: "This book provides an introduction to the differential geometry of curves and surfaces in three-dimensional Euclidean space"

The Ricci Flow Analytic Aspects

Author : Bennett Chow
ISBN : 9780821844298
Genre : Mathematics
File Size : 49. 43 MB
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Geometric analysis has become one of the most important tools in geometry and topology. In their books on the Ricci flow, the authors reveal the depth and breadth of this flow method for understanding the structure of manifolds. With the present book, the authors focus on the analytic aspects of Ricci flow. Some highlights of the presentation are weak and strong maximum principles for scalar heat-type equations and systems on manifolds, the classification by Bohm and Wilking of closed manifolds with 2-positive curvature operator, Bando's result that solutions to the Ricci flow are real analytic in the space variables, Shi's local derivative of curvature estimates and some variants, and differential Harnack estimates of Li-Yau-type including Hamilton's matrix estimate for the Ricci flow and Perelman's estimate for fundamental solutions of the adjoint heat equation coupled to the Ricci flow. The authors have tried to make some advanced material accessible to graduate students and nonexperts. The book gives a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. They have also attempted to give the appropriate references so that the reader may further pursue the statements and proofs of the various results. Also in the Mathematical Surveys and Monographs series: The Ricci Flow: An Introduction, Bennett Chow and Dan Knopf, Vol. 110, 2004. The Ricci Flow: Techniques and Applications. Part I: Geometric Aspects, Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, and Lei Ni, Vol. 135, 2007. The Ricci Flow: Techniques and Applications. Part III: Geometric-Analytic Aspects, Bennett Chow, Sun-Chin Chu, David Glickenstein, Christine Guenther, James Isenberg, Tom Ivey, Dan Knopf, Peng Lu, Feng Luo, and Lei Ni (forthcoming).

Stability Of Structures

Author : Z. P. Bažant
ISBN : 0486425681
Genre : Technology & Engineering
File Size : 68. 42 MB
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Exploration of principles and applications emphasizes nonelastic stability, focusing on problems of fracture and damage, thermodynamics of stability in irreversible systems, and other key areas. 700 exercise problems. 1991 edition.

Introduction To Differential Geometry For Engineers

Author : Brian F. Doolin
ISBN : 9780486281940
Genre : Mathematics
File Size : 78. 24 MB
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This outstanding guide supplies important mathematical tools for diverse engineering applications, offering engineers the basic concepts and terminology of modern global differential geometry. Suitable for independent study as well as a supplementary text for advanced undergraduate and graduate courses, this volume also constitutes a valuable reference for control, systems, aeronautical, electrical, and mechanical engineers.The treatment's ideas are applied mainly as an introduction to the Lie theory of differential equations and to examine the role of Grassmannians in control systems analysis. Additional topics include the fundamental notions of manifolds, tangent spaces, vector fields, exterior algebra, and Lie algebras. An appendix reviews concepts related to vector calculus, including open and closed sets, compactness, continuity, and derivative.

Differential Forms With Applications To The Physical Sciences

Author : Harley Flanders
ISBN : 9780486139616
Genre : Mathematics
File Size : 46. 12 MB
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A graduate-level text utilizing exterior differential forms in the analysis of a variety of mathematical problems in the physical and engineering sciences. Includes 45 illustrations. Index.

Differential Geometry

Author : R.W. Sharpe
ISBN : 0387947329
Genre : Mathematics
File Size : 74. 26 MB
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Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of "espaces généralisés" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.

Differential Manifolds

Author : Antoni A. Kosinski
ISBN : 9780486318158
Genre : Mathematics
File Size : 64. 49 MB
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Introductory text for advanced undergraduates and graduate students presents systematic study of the topological structure of smooth manifolds, starting with elements of theory and concluding with method of surgery. 1993 edition.

The Development Of Mathematics

Author : E. T. Bell
ISBN : 9780486152288
Genre : Mathematics
File Size : 64. 95 MB
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Time-honored study by a prominent scholar of mathematics traces decisive epochs from the evolution of mathematical ideas in ancient Egypt and Babylonia to major breakthroughs in the 19th and 20th centuries. 1945 edition.

Vector Analysis

Author : Louis Brand
ISBN : 9780486154848
Genre : Mathematics
File Size : 90. 44 MB
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This text was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into the subjects' manifold applications. 1957 edition. 86 figures.

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