 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/26j/d/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

(I^{S})^{- 1} = \frac{1}{W ^{2}} (1 + h_{y}^{2} - h_{x} h_{y} - h_{x} h_{y} 1 + h_{x}^{2}) .

Thus

2 H = tr ((I^{S})^{- 1} I I^{S})

vanishes exactly when

(1 + h_{y}^{2}) h_{xx} - 2 h_{x} h_{y} h_{x y} + (1 + h_{x}^{2}) h_{yy} = 0.

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