
antisymmetric tensor

ganithashaasthrathilum saidhaanthika bhauthikashaasthrathilum, oru tensor oru soochika upavibhaagathil (allengil athine sambandhichidatholam) oru soochika upavibhaagathil eathenkilum rund soochikakal parasparam maattumbol athu chinnathe (+/−) marimari maattukayaanengil antisemetric aanu. soochika upavibhagam saadhaaranayaayi ellah "koveriyant" allengil ellah "kontraavariyant" aayirikkanam.
udaaharanathinu,
soothravaakyam _ 1
tensor athinte aadya moonnu soochikakalumaayi bandhappett antisymetric aayirikkumbol ithu nilanilkkunnu.
oru tensor athinte soochikakalude "oro" jody kaimattatthinu keezhil adayaalam maattukayaanengil, tensor poornnamaayum (allengil poornnamaayum) antisemetric aanu. oordar formula _ 2-nte poornnamaayum antisymmetric koveriyant tensor feeldine deferential formula _ 2-phoom ennum poornnamaayum antisymmetric kontraavariyant tensor feeldine formula _ 2-vector feeld ennum vilikkam.
antisemetric, cemetric tensorukal.
soochikakalude formula 5, formula 6 ennivayil antisymmetric aaya oru tensor aykku soochikakalude formula 5, formula 6 ennivayil samamithiyaya oru tensor bii ulla sankochathinu samanamaaya 0 enna savisheshathayundu.
gadakangalude formula _ 9 ulla oru pothu tensorinu, oru jodi soochikakalude formula _ 5, formula _ 11 yuu ennivaykku samamitiyum antisymmetric bhaagangalum undu
 
mattu jody soochikakalkkum samanamaaya nirvachanangal nalkaam. bhagam" enna padam soochippikkunnathu pole, oru tensor ennathu oru nischitha jody soochikakalude samamiti bhaagathinteyum antisemetric bhaagathinteyum aakethukayaan,
soothravaakyam _ 12
notteshan.
aanti-simetriseshanulla oru hraswarekhaye oru jodi chathura brackettukalaal soochippikkunnu. udaaharanathinu, ekapaksheeyamaaya alavukalil, 2 kovariyant tensor m enna kramatthinu,
soothravaakyam _ 13
koodaathe oru oordar 3 koveriyant tensor tii,
soothravaakyam _ 14
eathenkilum 2,3 alavukalil iva ingane ezhuthaam
soothravaakyam _ 15
ivide formula _ 16 ennathu saamaanyavalkkaricha chronecker deltayaanu, koodaathe like soochikakalude sangrahathinaayi nammal ainsteen notteshan upayogikkunnu.
kooduthal pothuve, alavukalude ennam pariganikkathe, formula _ 17 soochikakalkku mukalilulla antisemetrisation ingane prakadippikkaam
soothravaakyam _ 18
pothuve, rank 2-leeii oro tenzer oru cemetric, aanti-cemetric jodiyaayi vighadippikkaam
formula _ 19
kooduthal sankeernamaaya samamithikalulla rank 3 allengil athil kooduthalulla tensorukalkku eee vighadanam pothuve shariyalla.
udaaharanagal.
poornnamaayum antisemetric tensorukalil iva ulppedunnu

