. (1.13) M n . ∧.η(M, g) . {ω i} {e i} η=ω 1∧· · · ∧ω n. (1.14) 2. 2.1. M n C(TM) M .M ??:C(TM)×C(TM)→C(TM) § (X, Y)7→? XY, : (i)? fX+hYZ=f? XZ+h? YZ; (ii)? X(fY+hZ) = (Xf)Y+f? xY+(Xh)Z+h? XZ, X, Y, Z∈ C(TM),f, h∈C(M),C(M) M .? XY Y X , . {x i} U?M . ? i= ??x i ?? i? j:= Γ kij? k, Γ jikdx k:=ω ji. (2.1) X=X i? i,Y=Y i? i ? XY=X i(? iY j+Γ jikY k)? j={X(Y j) +X iΓ jikY k}? j ={X(Y j) +X iω ji(Y)}? j. (2.2) (2.1) Γ kij ω ji ? 1 . ?. . ? XY ? XY=X iY j,i? j, Y j,i:=? iY j+Γ jikY k. ? T(X, Y) =? XY?? YX?[X, Y]. (2.3) T= 0, ?. (2.1) (2.2) ? M Γ kij= Γ kji. γ: (a, b)→M ,γ′(t) γ. V(t) γ(t) . ?γ′V(t) = 0 t , V γ. , γ:x i=x i(t), γ′(t) = dx i dt ? i, V(t) =V i(t)? i, V γ dV k dt +Γ kij dx i dt V j= 0, 1≤k≤n. , 2.1. M ?. γ: (a, b)→M V 0∈TM γ(t 0)(t 0∈(a, b)) , γ V V(t 0) =V 0.
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