Atnaujinkite slapukų nuostatas

El. knyga: Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups

(Université Lyon I), (Pennsylvania State University)
  • Formatas: PDF+DRM
  • Serija: Cambridge Tracts in Mathematics
  • Išleidimo metai: 13-Dec-2004
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9780511261886
Kitos knygos pagal šią temą:
Projective Differential Geometry Old and New: From the Schwarzian Derivative to the Cohomology of Diffeomorphism GroupsDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: Cambridge Tracts in Mathematics
  • Išleidimo metai: 13-Dec-2004
  • Leidėjas: Cambridge University Press
  • Kalba: eng
  • ISBN-13: 9780511261886
Kitos knygos pagal šią temą:

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

Emphasizing connections between classical projective differential geometry and contemporary mathematics, this work begins with a detailed discussion of the simplest differential projective invariant the Schwarzian derivative and its connection to the Virasoro algebra. Much of the book is devoted to one-dimensional projective differential geometry and related topics. A final chapter considers versions of the multi-dimensional Schwarzian derivative. Seven appendices cover background material. The book is for graduate students and researchers. Annotation ©2005 Book News, Inc., Portland, OR (booknews.com)

A rapid route for graduate students and researchers to the frontiers of contemporary research in this evergreen subject.

Ideas of projective geometry keep reappearing in seemingly unrelated fields of mathematics. This book provides a rapid route for graduate students and researchers to contemplate the frontiers of contemporary research in this classic subject. The authors include exercises and historical and cultural comments relating the basic ideas to a broader context.

Recenzijos

' this is an introduction to global projective differential geometry offering felicitous choice of topics, leading from classical projective differential geometry to current fields of research in mathematics and mathematical physics. The reader is guided from simple facts concerning curves and derivatives to more involved problems and methods through a world of inspiring ideas, delivering insights in deep relations. Historical comments as well as stimulating exercises occur frequently throughout the text, making it suitable for teachings.' Zentralblatt MATH

Daugiau informacijos

A rapid route for graduate students and researchers to the frontiers of research in this evergreen subject, first published in 2005.
Preface: why projective? ix
Introduction
1(25)
Projective space and projective duality
1(4)
Discrete invariants and configurations
5(3)
Introducing the Schwarzian derivative
8(5)
A further example of differential invariants: projective curvature
13(5)
The Schwarzian derivative as a cocycle of Diff(RP1)
18(3)
Virasoro algebra: the coadjoint representation
21(5)
The geometry of the projective line
26(21)
Invariant differential operators on RP1
26(3)
Curves in RP1 and linear differential operators
29(6)
Homotopy classes of non-degenerate curves
35(5)
Two differential invariants of curves: projective curvature and cubic form
40(2)
Projectively equivariant symbol calculus
42(5)
The algebra of the projective line and cohomology of Diff(S1)
47(22)
Transvectants
48(4)
First cohomology of Diff(S1) with coefficients in differential operators
52(5)
Application: geometry of differential operators on RP1
57(5)
Algebra of tensor densities on S1
62(4)
Extensions of Vect(S1) by the modules Fλ(S1)
66(3)
Vertices of projective curves
69(34)
Classic four-vertex and six-vertex theorems
69(7)
Ghys' theorem on zeroes of the Schwarzian derivative and geometry of Lorentzian curves
76(4)
Barner's theorem on inflections of projective curves
80(5)
Applications of strictly convex curves
85(5)
Discretization: geometry of polygons, back to configurations
90(7)
Inflections of Legendrian curves and singularities of wave fronts
97(6)
Projective invariants of submanifolds
103(50)
Surfaces in RP3: differential invariants and local geometry
104(12)
Relative, affine and projective differential geometry of hypersurfaces
116(7)
Geometry of relative normals and exact transverse line fields
123(10)
Complete integrability of the geodesic flow on the ellipsoid and of the billiard map inside the ellipsoid
133(8)
Hilbert's fourth problem
141(7)
Global results on surfaces
148(5)
Projective structures on smooth manifolds
153(26)
Definitions, examples and main properties
153(6)
Projective structures in terms of differential forms
159(2)
Tensor densities and two invariant differential operators
161(3)
Projective structures and tensor densities
164(5)
Moduli space of projective structures in dimension 2, by V. Fock and A. Goncharov
169(10)
Multi-dimensional Schwarzian derivatives and differential operators
179(35)
Multi-dimensional Schwarzian with coefficients in (2, 1)-tensors
179(6)
Projectively equivariant symbol calculus in any dimension
185(6)
Multi-dimensional Schwarzian as a differential operator
191(3)
Application: classification of modules Dλ2(M) for an arbitrary manifold
194(3)
Poisson algebra of tensor densities on a contact manifold
197(8)
Lagrange Schwarzian derivative
205(9)
Appendices
214(22)
A.1 Five proofs of the Sturm theorem
214(3)
A.2 The language of symplectic and contact geometry
217(4)
A.3 The language of connections
221(2)
A.4 The language of homological algebra
223(3)
A.5 Remarkable cocycles on groups of diffeomorphisms
226(3)
A.6 The Godbillon--Vey class
229(3)
A.7 The Adler--Gelfand--Dickey bracket and infinite-dimensional Poisson geometry
232(4)
References 236(11)
Index 247


Daugiau apie elektronines knygas Daugiau apie elektronines knygas
Pastovi nuoroda: https://www.kriso.lt/db/97805112618862e.html
Raktažodžiai: