Approximation of the second fundamental form of a hypersurface of a Riemannian manifold
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Approximation of the second fundamental form of a hypersurface of a Riemannian manifold David Cohen-Steiner — Jean-Marie Morvan. N° 4868 2 juillet 2003. ISSN 0249-6399. ISRN INRIA/RR--4868--FR+ENG. THÈME 2. apport de recherche.
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(384) 3å?nYs^tvWplm4^hil z|^
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(386) - m4r\z|z^
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(388) m¨n|e®¥Rp&w\gj^loXZYs^'tsplm^ il efdLn^
(389) klz p&¿g ßâm4r\z|z^
(390) dLn|theqt^
(391) d\i&n|^
(392) Üw:u å ^#]^
(393) dFn|efiFdÜnY\^m4iFdst~n p&dsmu¤n|Y\^iFz^
(394) ]¢iFzefdLn|^klz p&g mr\z|z^
(395) dFn tª¹« Ê .^ . MUS _a` °:µ °
(396) d QS * e QE\ Q MQÀv½
(397) ,l ½S R\j e
(398) D pSk^ÀZqp ! u¥mÀ 1Ce Q. DTQTik½Sjl\Q M ¹pÐtQvR
(399) QÀ
(400) QSMR mu tR QZR\j lm\#kÇ Q\Rv uÀ3R\jM½St6Ðtm#ÐtQaR\j lm\¹p kÇ Q\Rv . $ . . * Ì B[* UsrItQ uÑÐtQ QvQh R\Rv MQiQ Y R\jM½\t3Ðtm 18@ Y* U. 0#
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(402) gfgC:d\i* d.n|Ysp*nZnYs^ejdLn^kFz|plgWilm4rsz*p*n|r\z|^
(403) t0i&p'Y:u:W^
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(406) ^ZnY\^oef]Rilzn|p&dLnQ!ilz|ilEd ']
(407) î ^] ÊD ^]U îD '] îM îM îM îM îM îM']
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(409) p&z topFtp&d¤ejdLn^kFz|plg0«Åm4gjiFt^
(410) sm4r\z|z|^dLn
(411) ªmplgfgj^
(412) ±nY\^ B µ
(413) Ü o ² °/plt|tvim4eqp*n|^
(414) 8n|i6* acejl^
(415) dApctefd\kFr\gqp&z{tvrswstv^n
(416) &efnQeqtejdLn^
(417) z^Ut~n|efd\kcn|i¥Wds'pldApldsp&gjilkFilrstJnicnYs^ r\d\efn+dsilz|]plg:w\r\dsgj^l{XZY\^ kFi:i:/mp*n|^kFilz|uejdO Ysejm Y/nY\eqtcz^Utv^Up&z m Y¤mp&dOwW^iFd\^At^^
(418) ].ton|iwR^'nY\^.mp&n^
(419) klilz|ui&0tr\wspldsp&gjuLneqm t^4n tC Y\eqm Y/mildLn|plefdstejd/splzvn|ejmr\gjplzn|Y\^AmgjpFttoi&0t]i:i&nYOtvr\ws]pld\efilgq\tRn|Y\^AmgjpFttoi&0tr\wst^4n toil RiFtefnejl^z^Uplm YJpldsnY\^hm4gqplt|tZi&+RilgjuLYs^
(420) z p\ Y\^d8efn^4eqt~n tspm Ysplz|pFm¨n|^z|^e &Up*nejild#i& n|Y\^hd\iFz].p&g mpAud\m4iFgj^ z].ejtQpl\gCr\m^ unm4igj^l î{©\iFgfgji* efdsZk îLphmil]spFm¨nïtr\wst^4nQi&o * ejtïtplej'niwW^ R°:µ
(421) °
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(423) ( ]pld\d\eqp&d ].pld\e®iFgj * ( ^ ejgjg!rWtv^#nY\^ilgjgfi* ejd\k¤dsi&n|p&nejildst: #" ^4 dsi&n^Ut n|Y\^'t^
(424) mildsr\dW\p&]^dLn p&gilz|] il{nY\^'ef]]^z tvejild +«Øn|Ysp*nejtnY\^Atvu:]]^4n|zeqmhn|^dstilz efnY *pl» gfr\^Utejd n|Y\^d\ilz|].p&g!w\r\dsgj^61 0 *?¨ $^
(425) d\i&n|^
(426) tnY\^ ^
(427) efdskFp&zn^
(428) d ^dWil]ilz|\Y\eqt]Ï+d\^Ysplt x¼ E. 1,*¶x*) 61 0 *¶x. ÎäÙJÎRQ.
(429) U.
(430) ] ¼7@ " ¼, Ù » xh¼Üx " ( @ " 0 Ô~ $ » . . "( . Ò ^4n .wR^pr\d\efndsilz|]plgJl^Um¨n|ilzZ¥s^
(431) gj8iFd8nY\^Y:u:R^z tvr\z=plm^v* ^'\^d\iln^hw:u |n Y\^Aaplrstt ].plpFttim4eqp*n^U.n|inY\^hej]]A^
(432) z|tejildi&£*G 2 * Û 1 * ( eqt ^¥sd\^
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(435) µ L µ =<ØK< µ B d Q * e QÔ \ Q MQhÀ t gQSR\jl¡pS ½hQ¹p< \ Q MQÀ | ¹Àm
(436) sQ R\ mk
(437) M pSmk^À U QS Q ÐRÔRSQ½VÀpjlÀ
(438) QSDTmkpS\
(439) U Q QtlQwkÇjl
(440) sQ%pS\
(441) áqp UsrItQ » . *( d 1*¶x. . ". . . . d. e. Ïe. . " Ù». *(. x¼Ü s @ % 3 Ù »
(442) x¼
(443) Ü . Ò Î x . . .^x 0 4* ( E* Ò sÙ x Ü % 3 Ù
(444) x
(445) ÜÙ Î x . . .'x Πܥ@ 0A@ 3 Ù
(446) x
(447) ÜÙ Ù Î Ü=x . . .^x ٠Πܹܣ@ 0A@
(448) Ù Ù ÜÜ£@ " Ù x Ü. . x¼. ).
(449) µJµ ? µ ?
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(451) m4nilz tilQnYsejtoz|pl]^lªef¡R^
(452) z^
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(458) t!n|Y\^tvu:]]^4n|zu.il nYs^n^dWtviFz % 3 Ù7.
(459) x=.
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(461) m¨n|gfuw:u rstefd\k nY\^=pFm¨n n|Ysp*n n|Y\^hd\ilz|].p&gCw\r\dWgf^hiln|Y\^hY:u:W^
(462) z|tr\z=plm4^ceqtÒ p&kFz|pld\kleqp&d#efdE11 *T( ¨. ÙÙßê\èSë¨ç\ë. .
(463)
(464) . tlQSDQS VQS º \w. ]. &%/ ( âdn|Y\eqtQsplz|plklz p&\YJl0^pFttr\]^ nYWp*nQn|Y\^pl]w\eqp&dLnïtsplm^ ejt¿!%0C{XZY\^ompld\ildsejm
(465) p&gsplz|plgfgj^gjejt]¦ilV!%0 plds21!¿0#p&gjgji*tïn|iej^
(466) dLnefu#p*n ^
(467) pFm » Y#RilejdLnß)l1 å !Ñ0p&dW.!Ñ0C\pldsp&n ^
(468) plm Yl^U» m¨niFz å E1 å !%0C Ù¡!#0Ü ( Ù¡!Ñ0VÜ'plds}!Ñ0ª¶ î ¼1plz^±Wp&z p&gjgf^
(469) g l^
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(472) ildLn|plgWF^
(473) m4nilz0¥s^
(474) gj\t
(475) \p&dW ilds^cm
(476) p&d#^
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(478) m4nejild » x¼ ild Á 9 î * eqtp Y:u:W^
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(481) z àA ^hYspKF^ 3 \z èé sz èé @ " ÙÅ\z » xvsz ¼.Ü . . ^
(482) ].p&z| p&gqtviOnYWp*n " ÙÅ\z » x\z ¼ÜYspFtAp)splzvn|ejmr\gqp&z^4\z|^
(483) t|tvejild } âds\^^
(484) J!tefdWm4^ ¼ ejt mildstvn|pldLn
(485) L0^YspKl^iFd2* " ( \ *z èé ¼>@A y xW«= Y\^z|^ "§( \^d\iln^
(486) tïnYs^,ÒJ^
(487) :e® ef:efn|p'm4ildsd\^4ejild.ild.! 0 ¨ î+!^\^
(488) m4iF]WiLtv^cnYs^hz^Ut~n|zeqm¨n|efiFd#i&9 ¼ n. i *$efd8efn|t!n|pld\kl^
(489) dLn pldsd\ilz|].p&gªm4iF]WiFd\^dLn
(490) ¼>@ \z ¼ lx !^YspKl ^ " Ù=sz » xv\z * ¼sÜ9@ ~ \z * » Ù Ü. âd8ilnY\^
(491) z!!ilz \t
(492) % .
(493) . $#. &('*),+ 3 = ). . 9;8. 3. '. . (. ) /7=A-0/68:3+ ),9. . 8. 3. -. +. *) 3. = 03. + ). . . . . . . Ù 3 Ü. ]^Upltr\z^Ut0nY\^pKF^z p&kl^ildKà?iln|Y\^h*p&z|ejp&nejildi&nY\^hkFz|pFef^
(494) dLn!il efdn|Y\^hefz|^
(495) m4nejild8\z * » . . $#". &('*),+ 3 = ). 9;8. 3. (. 9. . . . *'*) 0/69. ^4n wW^pARilgjuLYs^
(496) z|ildi& !%0Csp&dW#gj^4n ÙZÜQe®n tZd\ilz|].p&gJmu:mgf^F ^tYsp&gjgJ^
(497) KplgfrWp*n^ ÙZÜx 3 x iFzpldLu,l^Um¨n|ilz.¥s^
(498) gj » x¼ Á ' efdsm^¤n|Y\^Omu:mgf^ Ù Z Ümp&d wW^)^
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