
homes-thampson valume

praamaanika pradaesaala jyaamitiloo, homes-thampson valume anedi vividha praamaanika pradaesaalaloo (oke parimaanam) unna setlanu poolchadaaniki anumatinche valume yokka bhavana. dheenini raymond dii parichayam chesaaru. homes mariyu anthony charless thampson.
nirvachanam.
oka praamaanika space formula _ 3loe kolavagala sett formula _ 2 yokka homes-thampson valume formula _ 1 anedi utpatti sett formula _ 4 yokka 2 "n"-dimensional kolatagaa nirvachinchabadindi, ikkada formula _ 5 anedi formula _ 6 yokka dual unit banthi (dual norm formula _ 7 yokka unit banthi).
symplectic (coordinate-free) nirvachanam.
homes-thampson vaalyuumnu coordinatelu lekunda nirvachinchavacchuh suutram _ 8 anedi "n"-dimensional real normed space formula _ 9loe kolavagala sett ayithe, daani homes-thampson vaalyuumnu parimaanam yokka samagra viluvagaa nirvachistaaru.
ikkada suutram _ 13 anedi vector space suutram _ 14 paie praamaanika symplectic roopam mariyu suutram _ 15 anedi suutram _ 16 yokka dwandwa unit banthi.
eee nirvachanam munupatidaaniki anugunamgaa untundi, endukante prati point suutram _ 17 kii leanier coordinatela suutram _ 18 ivvabadithe mariyu prati covector suutram _ 19 kii dual coordinatela suutram _ 20 ivvabadithe (tadwara aaa suutram _ 21), appudu praamaanika symplectic roopam suutram _ 22, mariyu valume roopam
dheeni integral sett formula _ 24 paie coordinate space formula _ 25 loe sett yokka saadhaarana valume matrame.
finsler manifoldslo valume.
marinta saadhaaranamgaa, finsler manifold formula _ 27 loe kolavagala sett formula _ 26 yokka homes-thampson vaalyuumnu ilaa nirvachinchavacchu
ikkada suutram _ 29 mariyu suutram _ 30 anedi catangent bundle suutram _ 31 paie praamaanika symplectic roopam. homes-thampson yokka valume yokka nirvachanam manifold yokka mottam valume mariyu daanilo unna geodesics (systolic asamaanatalu mariyu nimpe valuemlu vantivi) yokka podavu (athi chinna vakratalu) madhya linklanu sthaapinchadaaniki taginadi, endukante, leoville siddhaantam prakaram, geodesic pravaham cotangent bandillooni setla symplectic vaalyuumnu samrakshistundi.
coordinatelanu upayoginchi ganana.
suutram _ 32 anedi coordinate space formula _ 33 looni praantam ayithe, appudu prati point formula _ 34 vadda sparsaka mariyu catangent khaaliilu rendintinee suutram _ 33 thoo gurtinchavacchu. finsler metrik anedi nirantara function suutram _ 36, idhi prati point formula _ 34 kii (bahusha asamaana) pramaanam suutram _ 37 nuu istundi. upasamiti yokka homes-thampson vaalyuumnu ilaa lekkinchavacchu
ikkada prati point formula _ 34kii, sett formula _ 41 anedi formula _ 42 yokka dual unit banthi (dual norm formula _ 43 yokka unit banthi), baarla formula _ 44 anedi coordinate space loe oka upasamiti yokka saadhaarana vaalyuumnu suuchistumdi, mariyu formula _ 45 anedi anni coordinate differentials formula _ 46 yokka utpatti.
eee suutram mallii,-roopam suutram _ 47 anedi anni suutraala yokka bhedaala yokka utpatti (oka sanketam varaku) nundi samanam anae vaastavam nundi anusaristundi _ 48 akshaamsha suutram _ 49 mariyu vaati dwandwa akshaamsha suutram _ 50. appudu homes-thampson parimaanam suutram _ 52 yokka upasamiti suutram _ 51 yokka saadhaarana parimaanaaniki samanamga untundi.
shanta suutram.
suutram _ 26 anedi finsler manifoldlo oka saadhaarana praantam ayithe (antey, bantiki oka praantam homomorphic, convex sarihaddu mariyu suutram yokka prati jatha paayintla paayintla jatatho _ 26 thoo oka pratyaekamaina geodesic suutram), appudu daani homes-thampson vaalyuumnu saantaalo suutraanni upayoginchi suutram _ 26 yokka sarihaddu paayintla madhya maargam-podavu dhooram (suutram _ 26 venta) paramgaa lekkinchavacchu, idhi catangant bundle paie geodesic pravaham hamiltonian anae vaastavam meeda aadharapadi untundi.
saamaanyeekarana mariyu euclidean mariyu hasdorff kolatato poolika.
asalu rachayitalu homes-thampson valume kosam vaerae saadhaaraneekarananu upayoginchaaru. vaaru ikkada euclidean "enn"-baall yokka parimaanam dwara icchina viluvanu vibhajinchaaru, homes-thampson parimaanam praamaanika euclidean space formula _ 58 looni utpatti kolatato samanamga undela cheyadaaniki. eee vyaasam aaa sampradaayaanni anusarinchadu.
praamaanika pradaesaalaloo (ledhaa finsler manifolds) homes-thampson valume saadhaaraneekarinchabadithe, adhi eppuduu hasdorff kolatanu minchadu. idhi blaske-saantaalo asamaanata yokka parinaamam. sthalam euclidean (ledhaa remanian manifold) ayithe matrame samaanatvam untundi.

