Hauv kev ua lej, ua tiav manifold M yog Riemannian manifold rau qhov uas, pib ntawm txhua qhov taw tes p, koj tuaj yeem ua raws kab "ncaj" tsis muaj qhov kawg ntawm txhua qhov kev taw qhia.
Puas yog geodesically tiav?
Txhua qhov kev cog lus Riemannian manifolds thiab tag nrho cov homogeneous manifolds yog geodesically tiav. … Qhov tseeb, geodesic tiav thiab metric tiav yog sib npaug rau cov chaw no. Nov yog cov ntsiab lus ntawm Hopf–Rinow theorem.
Puas yog geodesic tshwj xeeb?
Rau txhua p 2 M thiab txhua v 2 TpM, muaj qhov tshwj xeeb geodesic, denoted v, xws li (0) =p, 0(0)=v, thiab lub npe ntawm yog qhov loj tshaj plaws tau, uas yog, tsis tuaj yeem txuas ntxiv. Peb hu v a maximal geodesic (nrog rau qhov pib v(0)=p thiab 0v(0)=v).
Puas yog geodesic txoj kev luv tshaj?
Nyob hauv geometry, geodesic (/ˌdʒiːəˈdɛsɪk, ˌdʒiːoʊ-, -ˈdiː-, -zɪk/) feem ntau yog nkhaus sawv cev rau qee qhov kev nkag siab shortest path (arc) ntawm ob lub ntsiab lus nyob rau saum npoo, los yog ntau tshaj nyob rau hauv ib tug Riemannian manifold.
Dab tsi yog qhov txawv ntawm geodetic thiab geodesic?
2 Teb. Muaj qhov sib txawv ntawm ob qho: Geodesy yog qhov chaw soj ntsuam thaj chaw thiab ntsuas, feem ntau ntawm qhov loj thiab suav nrog cov teeb meem longitude thiab latitude, thaum Geodesic yog hais txog kev nthuav tawm qee yam khoom ntawm cov kab ncaj. rau nkhaus thiab lwm qhov chaw.
