A general Fano hypersurface of degree d in P^n has rational curves of degree e with balanced restricted tangent bundle exactly when e exceeds (n-1)/(n+1-d), and quadrics have a separate parity rule.
Curves in P3 with good restriction of the tangent bundle
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Restricted tangent bundle of rational curves on projective hypersurfaces
A general Fano hypersurface of degree d in P^n has rational curves of degree e with balanced restricted tangent bundle exactly when e exceeds (n-1)/(n+1-d), and quadrics have a separate parity rule.