We prove an inequality between the sum of the Betti numbers of a complex projective manifold and its total curvature, and we characterize the complex projective manifolds whose total curvature is minimal. These results extend the classical theorems of Chern and Lashof to complex projective space.
Joseph Ansel Hoisington. "On the total curvature and Betti numbers of complex projective manifolds." Geom. Topol. 26 (1) 1 - 45, 2022. https://doi.org/10.2140/gt.2022.26.1