aam taur parr atee-javic aparivartaniya kaee gunaa

ack samanya roop seey atee-javic aparivartaniya manifold (aine. aich. aaee. aim.) ack atee-javic nishchit bindu aur ack atee-javic samooh kaa ack praakritik saamaanyikaran haye. antar koo shodhaatmak roop seey nimnanusar varnit kiya jaa sakata haih ack manifold sootra _ 1 key liye samanya roop seey hyperbolic honey key liye hamein yeh maanane kii anumati haye kii sootra _ 1 kii gatishilata paas kii gatishilata kii tulanaa mein tatasth haye, jise hyperbolic sett key liye anumati naheen haye. 1972 mein neel fenicial dwara nims koo pesh kiya gayaa thaa. iss aur baad key patron mein, fenicial saabit kartaa haye kii nims mein sthir aur asthir kaee gunaa hotey hain aur isase bhee mahatvapurna baat yeh haye kii nims aur unake sthir aur asthir kaee gunaa chhote-chhote gadbadi key tahat baney rahate hain. iss prakaar, vikshobh siddhant seey judee samasyaon mein, kuchh atisamvedansheelta gunon key saath aparivartaniya manifold maujood hain, jinka upayog ack gatishil pranali key baare mein gunaatmak jaankaari praapt karane key liye kiya jaa sakata haye.
paribhasha.
m" koo ack compact smooth manifold honey dein, "f": "m" "" m "" ack difiomorphism, aur "df": "tm" "" tm "" kaa antar "f".  m" key "f"-invariant submanifold "λ" koo samanya roop seey ack hyperbolic aparivartaniya manifold kahaa jaataa haye yadi "m" key sparshrekha bundle key "λ" parr pratibandh teen "df"-invariant subbundals key yog mein vibhajan koo sweekaar kartaa haye, ack sootra _ 1 kaa sparshrekha bundle haye, anya sthir bundle aur asthir bundle hain aur kramshah "e" s "aur" e "u" koo darshaaya jaataa haye. m" parr kuchh remanian metrick key sambandh mein, "df" seey "e" s "kaa pratibandh ack sankuchan honah chaahiye aur" df "seey" e "u" kaa pratibandh ack vistaar honah chaahiye, aur sootra _ 4 parr apekshaakrit tatasth honah chaahiye. iss prakaar, sootra _ 5 aur "c"> 0 aise sthiraank maujood hain kii
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