# 13. Let V be the canonical connection on R3 given by the directiona...

## Transcribed Text

13. Let V be the canonical connection on R3 given by the directional derivative. Define VxY = Vxy + 1XxY, where X denotes the cross-product. Show that V is a connection and find its torsion and curvature. 15. Suppose that O is a 1-form on R3 such that O ^ da III 0. Let X, Y are vector fields, such that a(x) = o(Y) = 0. Show that a(IX,Y]) = 0. 17. Let (x,y,2,t) are coordinates in R4 and X = Prove that any function f defined on all R4 satisfying x(f) = Y(f) = 0 is constant

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