Journal of Differential Geometry, Volumes 22-23

4-manifold a₁ algebraic bounded C₁ cohomology compact complex structure consider constant converges convex body coordinates Corollary corresponding curvature curve defined denote derivatives Differential Geometry dimension equation equivalent Euclidean exists fiber finite foliation follows formula function g₁ Gauss map given global harmonic maps hence holomorphic homology homothetic homotopy hyperbolic hypersurfaces immersion implies inequality integral intersection invariant isometric isomorphism Kähler Kähler manifold Lemma linear M₁ Math maximal direction metric minimal nonnegative nonzero normal bundle obtain orbits orthogonal parallel transport proof of Theorem Proposition prove rank result Riemannian manifold satisfies second fundamental form singularity smooth space sphere subbundle subgroup submanifolds subset subspace surface symmetric Teichmüller space tensor timelike topology totally geodesic U₁ V-manifold vanishes vector bundle vector field Z₂ zero