Geodesic
The Caratheodory Metric and its Majorant Metrics
Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 771-780

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One of the main purposes of the present paper is to provide a proof for the following statement:Theorem A. Let M be a complex manifold of a complex dimension n. Let be a fixed point in M such that there exists a square integrable holomorphic n-form a(z) on M with . 
Burbea, Jacob. The Caratheodory Metric and its Majorant Metrics. Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 771-780. doi: 10.4153/CJM-1977-080-9
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