Download or read book Integral Formulas in Riemannian Geometry written by Kentarō Yano and published by Marcel Dekker. This book was released on 1970 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integral Formulas in Riemannian Geometry written by Kentaro Yano and published by . This book was released on 2004 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Extrinsic Geometry of Foliations written by Vladimir Rovenski and published by Springer Nature. This book was released on 2021-05-22 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics. The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.
Download or read book Kinematic Formula in Riemannian Homogeneous Spaces written by D H Howard Howard and published by Oxford University Press, USA. This book was released on 2014-08-31 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows that much of classical integral geometry can be derived from the coarea formula by some elementary techniques. Howard generalizes much of classical integral geometry from spaces of constant sectional curvature to arbitrary Riemannian homogeneous spaces. To do so, he provides a general definition of an integral invariant'' of a submanifold of the space that is sufficiently general enough to cover most cases that arise in integral geometry. Working in this generality makes it clear that the type of integral geometric formulas that hold in a space does not depend on the full group of isometries, but only on the isotropy subgroup. As a special case, integral geometric formulas that hold in Euclidean space also hold in all the simply connected spaces of constant curvature. Detailed proofs of the results and many examples are included. Requiring background of a one-term course in Riemannian geometry, this book may be used as a textbook in graduate courses on differential and integral geometry.
Download or read book The Kinematic Formula in Riemannian Homogeneous Spaces written by Ralph Howard and published by American Mathematical Soc.. This book was released on 1993 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir investigates a method that generalizes the Chern-Federer kinematic formula to arbitrary homogeneous spaces with an invariant Riemannian metric, and leads to new formulas even in the case of submanifolds of Euclidean space.
Download or read book Differential and Riemannian Geometry written by Detlef Laugwitz and published by Academic Press. This book was released on 2014-05-12 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential and Riemannian Geometry focuses on the methodologies, calculations, applications, and approaches involved in differential and Riemannian geometry. The book first offers information on local differential geometry of space curves and surfaces and tensor calculus and Riemannian geometry. Discussions focus on tensor algebra and analysis, concept of a differentiable manifold, geometry of a space with affine connection, intrinsic geometry of surfaces, curvature of surfaces, and surfaces and curves on surfaces. The manuscript then examines further development and applications of Riemannian geometry and selections from differential geometry in the large, including curves and surfaces in the large, spaces of constant curvature and non-Euclidean geometry, Riemannian spaces and analytical dynamics, and metric differential geometry and characterizations of Riemannian geometry. The publication elaborates on prerequisite theorems of analysis, as well as the existence and uniqueness theorem for ordinary first-order differential equations and systems of equations and integrability theory for systems of first-order partial differential equations. The book is a valuable reference for researchers interested in differential and Riemannian geometry.
Download or read book Lectures On The Geometry Of Manifolds Third Edition written by Liviu I Nicolaescu and published by World Scientific. This book was released on 2020-10-08 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. It starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections on vector bundles and their curvatures, basic Riemannian geometry, calculus of variations, DeRham cohomology, integral geometry (tube and Crofton formulas), characteristic classes, elliptic equations on manifolds and Dirac operators. The new edition contains a new chapter on spectral geometry presenting recent results which appear here for the first time in printed form.
Download or read book Geometric Integration Theory written by Steven G. Krantz and published by Springer Science & Business Media. This book was released on 2008-12-15 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.
Download or read book Differential Geometry and Differential Equations written by Chaohao Gu and published by Springer. This book was released on 2006-11-15 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The DD6 Symposium was, like its predecessors DD1 to DD5 both a research symposium and a summer seminar and concentrated on differential geometry. This volume contains a selection of the invited papers and some additional contributions. They cover recent advances and principal trends in current research in differential geometry.
Download or read book Reconstructive Integral Geometry written by Victor Palamodov and published by Birkhäuser. This book was released on 2012-12-06 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers facts and methods for the reconstruction of a function in a real affine or projective space from data of integrals, particularly over lines, planes, and spheres. Recent results stress explicit analytic methods. Coverage includes the relations between algebraic integral geometry and partial differential equations. The first half of the book includes the ray, the spherical mean transforms in the plane or in 3-space, and inversion from incomplete data.
Download or read book Differential Geometry with Applications to Mechanics and Physics written by Yves Talpaert and published by CRC Press. This book was released on 2000-09-12 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential
Download or read book Differential Subordinations written by Sanford S. Miller and published by CRC Press. This book was released on 2000-01-03 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Examining a topic that has been the subject of more than 300 articles since it was first conceived nearly 20 years ago, this monograph describes for the first time in one volume the basic theory and multitude of applications in the study of differential subordinations."
Download or read book Integral and Discrete Transforms with Applications and Error Analysis written by Abdul Jerri and published by CRC Press. This book was released on 2021-11-19 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reference/text desribes the basic elements of the integral, finite, and discrete transforms - emphasizing their use for solving boundary and initial value problems as well as facilitating the representations of signals and systems.;Proceeding to the final solution in the same setting of Fourier analysis without interruption, Integral and Discrete Transforms with Applications and Error Analysis: presents the background of the FFT and explains how to choose the appropriate transform for solving a boundary value problem; discusses modelling of the basic partial differential equations, as well as the solutions in terms of the main special functions; considers the Laplace, Fourier, and Hankel transforms and their variations, offering a more logical continuation of the operational method; covers integral, discrete, and finite transforms and trigonometric Fourier and general orthogonal series expansion, providing an application to signal analysis and boundary-value problems; and examines the practical approximation of computing the resulting Fourier series or integral representation of the final solution and treats the errors incurred.;Containing many detailed examples and numerous end-of-chapter exercises of varying difficulty for each section with answers, Integral and Discrete Transforms with Applications and Error Analysis is a thorough reference for analysts; industrial and applied mathematicians; electrical, electronics, and other engineers; and physicists and an informative text for upper-level undergraduate and graduate students in these disciplines.
Download or read book Nonlinear Wave Equations written by Satyanad Kichenassamy and published by CRC Press. This book was released on 2021-05-30 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.
Download or read book The Theory and Applications of Harmonic Integrals written by W. V. D. Hodge and published by CUP Archive. This book was released on 1989-05-25 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1941, this book, by one of the foremost geometers of his day, rapidly became a classic. In its original form the book constituted a section of Hodge's essay for which the Adam's prize of 1936 was awarded, but the author substantially revised and rewrote it. The book begins with an exposition of the geometry of manifolds and the properties of integrals on manifolds. The remainder of the book is then concerned with the application of the theory of harmonic integrals to other branches of mathematics, particularly to algebraic varieties and to continuous groups. Differential geometers and workers in allied subjects will welcome this reissue both for its lucid account of the subject and for its historical value. For this paperback edition, Professor Sir Michael Atiyah has written a foreword that sets Hodges work in its historical context and relates it briefly to developments.
Download or read book A Mathematician and His Mathematical Work written by Shiing-Shen Chern and published by World Scientific. This book was released on 1996 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is about the life and work of Shiing-Shen Chern (1911-), one of the leading mathematicians of this century. The book contains personal accounts by some friends, together with a summary of the mathematical works by Chern himself. Besides a selection of the mathematical papers the book also contains all his papers published after 1988.
Download or read book Parabolic Equations on an Infinite Strip written by Watson and published by Routledge. This book was released on 2017-10-02 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on solutions of second order, linear, parabolic, partial differentialequations on an infinite strip-emphasizing their integral representation, their initialvalues in several senses, and the relations between these.Parabolic Equations on an Infinite Strip provides valuable information-previously unavailable in a single volume-on such topics as semigroup property.. . the Cauchy problem ... Gauss-Weierstrass representation . .. initial limits .. .normal limits and related representation theorems ... hyperplane conditions .. .determination of the initial measure .. . and the maximum principle. It also exploresnew, unpublished results on parabolic limits . . . more general limits ... and solutionssatisfying LP conditions.Requiring only a fundamental knowledge of general analysis and measure theory, thisbook serves as an excellent text for graduate students studying partial differentialequations and harmonic analysis, as well as a useful reference for analysts interested inapplied measure theory, and specialists in partial differential equations.
