2023/03/11 by Ebenfelt, Peter, Xiao, Ming, Xu, Hang
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2303.06408
This paper concerns obstruction flatness of hypersurfaces Σ that arise as unit sphere bundles S(E) of Griffiths negative Hermitian vector bundles (E, h) over Kähler manifolds (M, g). We prove that if the curvature of (E, h) satisfies a splitting condition and (M,g) has constant Ricci eigenvalues, then S(E) is obstruction flat. If, in addition, all these eigenvalues are strictly less than one and (M,g) is complete, then we show that the corresponding ball bundle admits a complete Kähler-Einstein metric.