Differential Systems And Isometric Embeddings

Author : Phillip A. Griffiths
Publisher : Princeton University Press
ISBN 13 : 1400882109
Total Pages : 238 pages
Book Rating : 4.06/5 ( download)

DOWNLOAD NOW!

Download or read book Differential Systems and Isometric Embeddings.(AM-114), Volume 114 written by Phillip A. Griffiths and published by Princeton University Press. This book was released on 2016-03-02 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of exterior differential systems provides a framework for systematically addressing the typically non-linear, and frequently overdetermined, partial differential equations that arise in differential geometry. Adaptation of the techniques of microlocalization to differential systems have led to recent activity on the foundations of the theory; in particular, the fundamental role of the characteristic variety in geometric problems is now clearly established. In this book the general theory is explained in a relatively quick and concrete manner, and then this general theory is applied to the recent developments in the classical problem of isometric embeddings of Riemannian manifolds.

Author : Phillip Griffiths
Publisher :
ISBN 13 : 9780691084299
Total Pages : 225 pages
Book Rating : 4.97/5 ( download)

DOWNLOAD NOW!

Download or read book Differential Systems and Isometric Embeddings written by Phillip Griffiths and published by . This book was released on 1987 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of exterior differential systems provides a framework for systematically addressing the typically non-linear, and frequently overdetermined, partial differential equations that arise in differential geometry. Adaptation of the techniques of microlocalization to differential systems have led to recent activity on the foundations of the theory; in particular, the fundamental role of the characteristic variety in geometric problems is now clearly established. In this book the general theory is explained in a relatively quick and concrete manner, and then this general theory is applied to the recent developments in the classical problem of isometric embeddings of Riemannian manifolds.

Author : Qing Han
Publisher : American Mathematical Soc.
ISBN 13 : 0821840711
Total Pages : 278 pages
Book Rating : 4.19/5 ( download)

DOWNLOAD NOW!

Download or read book Isometric Embedding of Riemannian Manifolds in Euclidean Spaces written by Qing Han and published by American Mathematical Soc.. This book was released on 2006 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of the existence of isometric embeddings of Riemannian manifolds in Euclidean space is already more than a century old. This book presents, in a systematic way, results both local and global and in arbitrary dimension but with a focus on the isometric embedding of surfaces in ${\mathbb R}^3$. The emphasis is on those PDE techniques which are essential to the most important results of the last century. The classic results in this book include the Janet-Cartan Theorem, Nirenberg's solution of the Weyl problem, and Nash's Embedding Theorem, with a simplified proof by Gunther. The book also includes the main results from the past twenty years, both local and global, on the isometric embedding of surfaces in Euclidean 3-space. The work will be indispensable to researchers in the area. Moreover, the authors integrate the results and techniques into a unified whole, providing a good entry point into the area for advanced graduate students or anyone interested in this subject. The authors avoid what is technically complicated. Background knowledge is kept to an essential minimum: a one-semester course in differential geometry and a one-year course in partial differential equations.

Author : Phillip A. Griffiths
Publisher : Princeton University Press
ISBN 13 : 9780691084305
Total Pages : 244 pages
Book Rating : 4.00/5 ( download)

DOWNLOAD NOW!

Download or read book Differential Systems and Isometric Embeddings written by Phillip A. Griffiths and published by Princeton University Press. This book was released on 1987-05-21 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of exterior differential systems provides a framework for systematically addressing the typically non-linear, and frequently overdetermined, partial differential equations that arise in differential geometry. Adaptation of the techniques of microlocalization to differential systems have led to recent activity on the foundations of the theory; in particular, the fundamental role of the characteristic variety in geometric problems is now clearly established. In this book the general theory is explained in a relatively quick and concrete manner, and then this general theory is applied to the recent developments in the classical problem of isometric embeddings of Riemannian manifolds.

Author : Kichoon Yang
Publisher : Springer Science & Business Media
ISBN 13 : 9401580685
Total Pages : 206 pages
Book Rating : 4.87/5 ( download)

DOWNLOAD NOW!

Download or read book Exterior Differential Systems and Equivalence Problems written by Kichoon Yang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a concise yet elementary account of exterior differential system theory so that it can be quickly applied to problems. The first part of the monograph, Chapters 1-5, deals with the general theory: the Cartan-Kaehler theorem is proved, the notions of involution and prolongation are carefully laid out, quasi-linear differential systems are examined in detail, and explicit examples of the Spencer cohomology groups and the characteristic variety are given. The second part of the monograph, Chapters 6 and 7, deals with applications to problems in differential geometry: the isometric embedding theorem of Cartan-Janet and its various geometric ramifications are discussed, a proof of the Andreotti-Hill theorem on the O-R embedding problem is given, and embeddings of abstract projective structures are discussed. For researchers and graduate students who would like a good introduction to exterior differential systems. This volume will also be particularly useful to those whose work involves differential geometry and partial differential equations.

Author : Deane Yang
Publisher : American Mathematical Soc.
ISBN 13 : 0821824333
Total Pages : 109 pages
Book Rating : 4.37/5 ( download)

DOWNLOAD NOW!

Download or read book Involutive Hyperbolic Differential Systems written by Deane Yang and published by American Mathematical Soc.. This book was released on 1987 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Cartan-Kähler theorem demonstrates that certain real analytic exterior differential systems--ones which Cartan dubbed "involutive"--admit local real analytic solutions. The proof reduces the system to a set of determined systems of PDE's which are then solved using the Cauchy-Kovalevski theorem. The subtlety in the theorem and in the definition of involutivity lies in checking that the "solution" obtained from the determined systems does in fact satisfy the original differential system.

Author : Robert L. Bryant
Publisher : Springer Science & Business Media
ISBN 13 : 1461397146
Total Pages : 483 pages
Book Rating : 4.44/5 ( download)

DOWNLOAD NOW!

Download or read book Exterior Differential Systems written by Robert L. Bryant and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object.

Author : P.A. Griffiths
Publisher : Springer Science & Business Media
ISBN 13 : 1461581664
Total Pages : 348 pages
Book Rating : 4.66/5 ( download)

DOWNLOAD NOW!

Download or read book Exterior Differential Systems and the Calculus of Variations written by P.A. Griffiths and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 15 0. PRELIMINARIES a) Notations from Manifold Theory b) The Language of Jet Manifolds c) Frame Manifolds d) Differentia! Ideals e) Exterior Differential Systems EULER-LAGRANGE EQUATIONS FOR DIFFERENTIAL SYSTEMS ~liTH ONE I. 32 INDEPENDENT VARIABLE a) Setting up the Problem; Classical Examples b) Variational Equations for Integral Manifolds of Differential Systems c) Differential Systems in Good Form; the Derived Flag, Cauchy Characteristics, and Prolongation of Exterior Differential Systems d) Derivation of the Euler-Lagrange Equations; Examples e) The Euler-Lagrange Differential System; Non-Degenerate Variational Problems; Examples FIRST INTEGRALS OF THE EULER-LAGRANGE SYSTEM; NOETHER'S II. 1D7 THEOREM AND EXAMPLES a) First Integrals and Noether's Theorem; Some Classical Examples; Variational Problems Algebraically Integrable by Quadratures b) Investigation of the Euler-Lagrange System for Some Differential-Geometric Variational Pro~lems: 2 i) ( K ds for Plane Curves; i i) Affine Arclength; 2 iii) f K ds for Space Curves; and iv) Delauney Problem. II I. EULER EQUATIONS FOR VARIATIONAL PROBLEfiJS IN HOMOGENEOUS SPACES 161 a) Derivation of the Equations: i) Motivation; i i) Review of the Classical Case; iii) the Genera 1 Euler Equations 2 K /2 ds b) Examples: i) the Euler Equations Associated to f for lEn; but for Curves in i i) Some Problems as in i) sn; Non- Curves in iii) Euler Equations Associated to degenerate Ruled Surfaces IV.

Author : Qing Han
Publisher : American Mathematical Society(RI)
ISBN 13 : 9781470413576
Total Pages : 278 pages
Book Rating : 4.74/5 ( download)

DOWNLOAD NOW!

Download or read book Isometric Embedding of Riemannian Manifolds in Euclidean Spaces written by Qing Han and published by American Mathematical Society(RI). This book was released on 2014-05-21 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of the existence of isometric embeddings of Riemannian manifolds in Euclidean space is already more than a century old. This book presents, in a systematic way, results both local and global and in arbitrary dimension but with a focus on the isometric embedding of surfaces in ${\mathbb R} DEG

Author : Michael Eastwood
Publisher : Springer Science & Business Media
ISBN 13 : 0387738312
Total Pages : 565 pages
Book Rating : 4.14/5 ( download)

DOWNLOAD NOW!

Download or read book Symmetries and Overdetermined Systems of Partial Differential Equations written by Michael Eastwood and published by Springer Science & Business Media. This book was released on 2009-04-23 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This three-week summer program considered the symmetries preserving various natural geometric structures. There are two parts to the proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection.