Analysing the Wu metric on a class of eggs in Cn -1
Proceedings of the Indian Academy of Sciences: Mathematical Sciences
We study the Wu metric on convex egg domains of the form where m > 1/2, m ≠ 1. The Wu metric is shown to be real analytic everywhere except on a lower dimensional subvariety where it fails to be C2-smooth. Overall however, the Wu metric is shown to be continuous when m = 1/2 and even c1-smooth for each m > 1/2, and in all cases, a non-Kähler Hermitian metric with its holomorphic curvature strongly negative in the sense of currents. This gives a natural answer to a conjecture of S. Kobayashi and H. Wu for such E2m.
Balakumar, G. P. and Mahajan, Prachi, "Analysing the Wu metric on a class of eggs in Cn -1" (2017). Journal Articles. 2611.