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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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extension of Riemannian metric on real affine variety

Given a Riemannian metric $g$ on the real part $X_R$ of a real affine variety $X$, is there a "natural" way to extend $g$ to be a Riemannian metric on $X$?
Xiaoyang Chen's user avatar