2022/01/31 by Chen, Haojie, Nie, Xiaolan · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2201.13083
Motivated by a recent work of Chen-Zheng [8] on Strominger space forms, we prove that a compact Hermitian surface with pointwise constant holomorphic sectional curvature with respect to a Gauduchon connection ∇t is either Kähler, or an isosceles Hopf surface with an admissible metric and t=-1 or t=3. In particular, a compact Hermitian surface with pointwise constant Lichnerowicz holomorphic sectional curvature is Kähler. We further generalize the result to the case for the two-parameter canonical connections introduced by Zhao-Zheng [30], which extends a previous result by Apostolov-Davidov-Muškarov [2].