Nyob rau hauv lej, covariant derivative yog ib txoj kev qhia ib tug derivative nrog tangent vectors ntawm ib tug manifold.
Covariant derivative siv rau dab tsi?
uas yog ib qho kev qhia dav dav ntawm cov cim feem ntau siv txhawm rau txheeb xyuas qhov sib txawv ntawm vector muaj nuj nqi hauv peb qhov ntev, qee zaum kuj siv. (Weinberg 1972, p. 104).
Lub ntsiab lus ntawm lub cev ntawm cov sib txawv yog dab tsi?
Covariant derivative piav qhia qhov gradient ntawm vector teb (piv txwv li, qhov cuam tshuam ntawm kev siv tus neeg teb xov tooj gradient vector) rau vector, thiab kom suav nrog ib feem derivatives raws li kev koom tes cov lus qhia ntawm ob qho tib si vector Cheebtsam thiab lub hauv paus vectors.
Qhov txawv ntawm covariant derivative thiab dag derivative yog dab tsi?
Cia siab tias qhov no qhia txog qhov sib txawv loj ntawm ob qhov kev sib txawv: cov sib txawv ntawm cov khoom siv yuav tsum tau siv los ntsuas seb lub tensor puas yog thauj mus los, thaum lub dag derivative ntsuas seb lub tensor yog invariant nyob rau hauv diffeomorphisms nyob rau hauv kev coj ntawm lub vector ξa.
Covariant derivative ntawm scalar yog dab tsi?
Ntau qhov ntau, rau qhov tensor ntawm arbitrary qeb, covariant derivative yog ib feem derivative ntxiv rau kev sib txuas rau txhua qhov ntsuas siab, rho tawm kev sib txuas rau txhua qhov ntsuas qis.
