Small overall thickness: minimize the strain differential between the inner and outer surfaces of the curve.
Thin individual plies: as above, but for each solid layer of wood.
Fine-grained wood species: to enable both of the above while retaining a solid structure.
Flexible glue: allow for the outer layer to "stretch" past the inner layer.
Grain oriented along the intended curve axis: if you think of the wood grain structure as a bundle of columns, they bend much more readily between the columns than along the columns.