let x a point on complex manifold X, z_j a coordinate system at x , E a holomorphic bundle and let h_α be a holomorphic frame of E. After replacing h_α by suitable linear combinations with constant coefficients we may assume that h_ α is an orthonormal basis of E_{x}. Then an inner product <h_α, h_β > have an expansion :(adsbygoogle = window.adsbygoogle || []).push({});

<h_α, h_β > = δ_αβ + Ʃ ( a_jαβ z_j + a'_jαβ z_j) + O( |z|^2 ) (1)

for some complex coefficients a_jαβ and a'_jαβ .

I would like to understandd how did he get the expression (1) ?

Thnx for your answers..

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# Normal coordinate frame

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