геодезик чизиқлар. гаусс-бонне теоремаси

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1446981736_62086.doc ô g r r r r = ( ) t t r ¢ ¢ r ( ) t g ( ) t g ( ) t r r ( ) t r r r r = ( ) t r ¢ r ( ) t ( , ) r r ¢ ¢ r r ( , ) ( , ) r r r r ¢ ¢ ¢ = ¢ ¢ ¢ = r r r r 2 0 | ( )| ( , ) r r r ¢ = ¢ ¢ r r r t r r r r = ( ) t s s t = ( ) r r r r = ( ) s b a + = t s s s t = ( ) 0 ) ( > ¢ t s 0 ) ( ¢ t s 0 = ¢ ¢ s b a …

r t r t { } 0 , 2 , 2 ) , , ( y x z y x gradf = 2 2 ) , , ( r y x z y x f - + = 0 ) , , ( = z y x f ) ( t r ¢ ¢ r 0 = a 0 = a 2 s 2 2 2 2 r z y x = + + 2 1 , e e r r 2 1 sin cos ) ( e t r e t r t r r r + = r ( ) r t = | | r r ( ) ( ) t e t r e t r t r r r r r r - = - - = ¢ ¢ 2 1 sin cos ) ( t r r ( ) t r r 2 1 …

+ = + = 3 2 3 1 3 2 3 2 ) , ( ) . ( p c p c p c p c v u u v - = - r r r r p n c n n p n c n n v u r r r r r 2 2 1 2 2 1 1 1 , + = + = n n n n n n n n n n n c p n n p c n n n n v u r r r r r r r r r ) ( ] , [ ] , [ ] , [ 1 2 2 1 2 2 1 1 1 2 2 1 2 2 1 1 1 2 2 1 2 2 1 1 - = = - = + = ] , [ p c n r r r …

оҳа учта геодезик чизиқлар билан чегараланган ҳолни кўрайлик. геодезик чизиқлар учун бўлганлигидан гаусс-бонне теоремасига кўра 112. 113. кўринишга келади. бу ҳолда соҳа геодезик учбурчак бўлиб, унинг ички бурчаклари лар учун ўринли бўлади. шунинг учун юқоридаги формула 114. 115. кўринишга келади. бу ерда бўлса (мисол учун сирт текислик бўлса) тенгликни ҳосил қиламиз. 116. (2) (5) _1044513726.unknown _1047394077.unknown _1286009906.unknown _1286010520.unknown _1427710657.unknown _1427711332.unknown _1427712660.unknown _1427715768.unknown _1427715909.unknown _1427716102.unknown _1427716153.unknown _1427716430.unknown _1427716536.unknown _1427716561.unknown _1427716500.unknown _1427716244.unknown _1427716120.unknown _1427716011.unknown _1427716058.unknown _1427715960.unknown _1427715870.unknown _1427715892.unknown _1427715857.unknown _1427715512.unknown _1427715565.unknown _1427715618.unknown _1427715561.unknown _1427715448.unknown _1427715495.unknown _1427712811.unknown _1427711457.unknown _1427712026.unknown _1427712525.unknown _1427711577.unknown _1427711407.unknown _1427711437.unknown _1427710999.unknown _1427711234.unknown _1427711285.unknown _1427711312.unknown _1427711181.unknown _1427711205.unknown _1427711013.unknown _1427710812.unknown _1427710879.unknown _1427710917.unknown _1427710849.unknown _1427710741.unknown _1427710790.unknown _1427710738.unknown _1286010811.unknown _1286012971.unknown _1286013236.unknown _1286013310.unknown _1286013440.unknown _1286013571.unknown _1286013593.unknown _1286013389.unknown _1286013279.unknown _1286013120.unknown _1286013186.unknown _1286013108.unknown _1286012761.unknown _1286012910.unknown _1286012918.unknown _1286012645.unknown _1286012667.unknown _1286012680.unknown _1286010868.unknown _1286012614.unknown _1286010565.unknown _1286010769.unknown _1286010802.unknown _1286010602.unknown _1286010709.unknown _1286010548.unknown _1286010186.unknown _1286010285.unknown _1286010336.unknown _1286010432.unknown _1286010451.unkn

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1446981736_62086.doc ô g r r r r = ( ) t t r ¢ ¢ r ( ) t g ( ) t g ( ) t r r ( ) t r r r r = ( ) t r ¢ r ( ) t ( , ) r r ¢ ¢ r r ( , ) ( , ) r r r r ¢ ¢ ¢ = ¢ ¢ ¢ = r r r r 2 0 | ( )| ( , ) r r r ¢ = ¢ ¢ r r r t r r r r = ( ) t s s t = ( ) r r r r = ( ) s b a …

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