The Campana-Peternell conjecture asserts that every smooth connected complex Fano manifold with nef tangent bundle is rational
homogeneous, hence isomorphic to 
for a connected semisimple complex algebraic
group and a parabolic subgroup.
Campana-Peternell Conjecture
See also
Albanese Variety, Fano Manifold, Nef Vector Bundle, Rational Homogeneous Variety, Tangent Bundle, Universal CoverExplore with Wolfram|Alpha
References
Muñoz, R.; Occhetta, G.; Solá Conde, L. E.; Watanabe, K.; and Wiśniewski, J. A. "A Survey on the Campana-Peternell Conjecture." Rend. Istit. Mat. Univ. Trieste 47, 127-185, 2015. https://doi.org/10.13137/0049-4704/11223.Cite this as:
Weisstein, Eric W. "Campana-Peternell Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Campana-PeternellConjecture.html