Question

Find extremals

b) J(y) oe2(y - y2)d, y(0)=1, y(3) free c) J(y) Jo2+'y )d, y(0) = , y(1) free. d) J(y) 22y2 - y2)d, y(1) 1, y(e) free. (1) X= B (ii) y is a geodesic; (iii) Xp is not zero and is parallel along 6.5 Let y be a curve with Y(0) = P, T(1) = Q. If Xe T,M, let X be the parallel translate ofX along y. Define y: T,M --- TqM by y*= X(1) (a) Prove that y* is a linear transformation. (b) Prove that y# is an isometry, that is, that

Answer 1

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