On Ribaucour transformations for hypersurfaces
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(255) z\yMz|~n°
(256) $ 7
(257) &} p 7 ºHr s2t®s2t yHyH A r s2t yHwt ¼Ü»0¤z w¤~atwx¸t~ 9
(258)
(259) $A m\ 9 A J 7 9
(260)
(261) 9 x
(262) m
(263) $ m ¼ A m 9 A } W7dº < $ A } ¼ > ®V tyH vt s¹yHsQHztz&st}vyHz $<#>?>@>?< ~wxtHat T$9 º A 32wxyH 9kÆH¼ A t\Mts2t6Mzz|yn ~xt´ v2u2·z|v2~2¶}yH¤s2Ks[¤zMat[n9
(264) A . . . . . . k . uwyHutwxtz+
(265). . ³9¹ÄwyHuy{z|xyMgÆn¾Æn°!xs2t7v2u¹snutwKzv2w|}kMt J( sMz&s2t>}yHy2 º'.
(266) k l ³Ù}6 xs2t }v23yHz wt®yMz|~n°st J( z>Fsnutwz|v2w}kHtu~w~t y $ ´È $ u l ³k} $ 7
(267) $ 7
(268) ´ }yHw~ ¼n° [¤z®t~w&}v23yHgMatT 7
(269) =D&mo9
(270)
(271) $A 5. ºM°'xs2t J( z ±yHut®zv2z|t 7y}>snutwu2¤~2t_z|t ~Kz u2wx uv2wxM~vwtz M~z|s¨ w.l ³Ù}(}yMw tz ¼*o $<U>?>?>@< o°2s2t }v23yHz ¬~wt\2twR5 °2s2t J( sHz 0Î twyu2wx uv2wxM~vwt\y~}ªvu2¤¶ . . l ³k}}yMw nz|x ntz ts3©at
(272) 7
(273) 7 >?>@> 7
(274) 7M n°s2t±@ tHt6 2yH 2Î twy6u2wu3~Ov2wxHv2wxt7y}8vu2¤P °2 yHwwxtz|uyM&yRJ 7 >@>?> 7 J l ³ xs2t\Ht2t w¬Hzt&u2wx uv2wxM~vwtzsat >v2xu2K96yH2ta. E _.
(275) I^ pUea#g [ E fUG _ N*7 [È1 [
(276) [ g) I;
(277) E%$ `_xaUc (9;5 $<#>@>?>?< 5 A 7:99 zQ5 $ yaz 5 < z|Q5 $ z|Q5 #< yazt5 $< 5 É <#>?>@>?< 5 ]A> J( E [ [
(278) [ g) =I;
(279) %E $ `_ # E Ptc
(280) sU.
(281) ?f [ *GH] [ G@GHc [ U] E^[ Iz `_ID ( E f [ t_ eGHc E f J( E E Fy a#c
(282) r
(283) . $ Q 7 yaz 5 $ m $ < 7 }yHw6 ¼ < 9
(284) H¼ A 7 z|Q5 $ m\ < 7 99 zQ5 $ m $A<
(285) 9 HÆ A . 4 !. . . . . . . 7 y{z 5 m z|S5 m
(286) º Nv¼ < K7
(287) s 5 m
(288) = $ 5.Wm
(289) =D Æ* N >. 9
(290) A 9
(291) A. wt%$47 7º~3 7o¢}yMwÆ*NvN( r st7¸wKz }v22[tnK3}yMw y}v z Hat> & 7 5 s2 twt{° 7Qz|S5 $ n7+º-}yMwS7 ¼¢³ }yMy~ z }wyM 99%Æ A °9kÆ A ~3b99Æ ' A xs~ °º 8° ~wxt=Matn~9
(292) H¼ A P9
(293) HÆ A °'stwt D9;5 A wt6¶Ðt wtn¤~2t7}v2xyMz ³9´yMwKt wy[Mts2t_~wxt7v2uz|v2~2¶}yH¤2z J( yn ~Hzxz|yn¤~xt xy)( n 3~vyMv2ww~z9}yHwx~xyH¨°2 t6yH3z|ntws2t }yMy2tÍnu2wtzxz|yHz + 7 $ m m¹¼ 9 $ z|Q 5 $ m $ ya z 5 $A m 9 A 4 ! 57 @r s2t u2wx uav2wxM~vwtzy~}. . $. º».
(294) . 7 . . ¬ ¬¼¼ ¹m ¼y{z 5 $ }} 7d7¼º $ } mÆ . V t 2¸wKzyMz|¤tws2 t-Hztz![s2Ks~2}v23yHz ~wxt 2yM Î twy!¯at 7 ® ° t_yH vt\}wyM r styHwxt ¼¾»>s s2t\}v2xyMz ~wxt&Mat9
(295) A P
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