A Hermitian metric on hyperbolic complex manifolds

Key Points

• The defined Hermitian metric is distance decreasing under holomorphic mappings, enhancing its utility.
• This method differs from Wu's classical construction, potentially offering superior regularity properties.
• The metric's distinctiveness lies in its application to Kobayashi hyperbolic manifolds, broadening its significance.
• This research provides a novel framework for understanding metrics in hyperbolic complex manifolds.