Read e-book online An Introduction to Lorentz Surfaces (De Gruyter Expositions PDF

By Tilla Weinstein

ISBN-10: 311014333X

ISBN-13: 9783110143331

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Additional info for An Introduction to Lorentz Surfaces (De Gruyter Expositions in Mathematics 22)

Example text

1 co~ue pr@c@demment. CHAPITRE V EXISTENCE DE V01SINAGES TUBULAIRES Dams ce chapitre, nous montrons que la construction ~e voisinages tubulaires d'une sous-vari@t@ d'une vari@t6 donn@e faite dams [ I~ (Chapitre IV) peut se parti- culariser au eas des structures @tal6es. ,,I,,,,~PR0~AGAT~URS ETALES (Layer-spray) Dgfinition I. Soit M une vari6t@ @tal6e model6e sur est une section du fibr6 double tangent br6 tangent sur (~,T,T',T") M v@rifiant les propri6t6s (iii) U~ T2M & la vari6t6 ~(~,KT) M (i) (i±), (iii).

Pi(I) = (1,1 ..... I .... ) Pi(I) quel que soit est situ6 dans est situ4 dans t < I , il existe un voisinage E° - E It de t dans [0,1] tel que 43 P1(It) soit contenu dans un espace de dimension finie. pi(t) = (~i(t), , IPl(t)lo 2 ,< Soit ~ rune 2t~(t 2) ..... Z n>/ I 9 ntn-1~(t n) .... ) ~? ant l'application <_ 0 nous renvoyons h [11]) ~r [ 2] et . > r Posons f(x) = = + p1(~r(l~ Io)) Nous remarquons que : a) f est une application E ~ E 0 b)~est do classe co C , en dehors de 0 . 0 l'identit6 en dehors de E (r) 0 s) f( i(E)- {o})ci(E) d) La restriction & E - {0} de f est une L(IdE) application.

DIFFE0~0RPHISME DE BESSAGA Th@or&me I. Soit E(z) la boule de centre morphisme de classe et tel que C°° , 0 et de rayon ~ : E - 101 ~ E r de E • I1 existe un diff@o- qui est l'identit@ en dehors de (~ - id) soit localement contenu dans un e s ~ c e de dimension finie. D@monstration. Un point de E(r) E, x ~est repr@sent@ par une suite de nombre r@els 42 x = {x 1 . . . xn .... Z ) ; n£1g Soit g tun n o m b r e > 0 x 2 <~}. n qui sera choisi ult6rieurement ~Xn 2 soit E = ix, ~=(x 1 ..... x n ....

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An Introduction to Lorentz Surfaces (De Gruyter Expositions in Mathematics 22) by Tilla Weinstein


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