Let $X$ be a complex manifold with a Hermitian metric. Is there a "complex" analogue of geodesics on $X$ which is of any interest? For example, is anything known about holomorphic maps $f : \mathbb C \rightarrow X$ satisfying $\nabla_{df/dz} (df/dz) = 0$ (which, naively, looks like a reasonable complex analogue of the geodesic condition)?
2026-05-16 21:15:48.1778966148
Holomorphic analogue of geodesics
109 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in COMPLEX-ANALYSIS
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