We introduce a new invariant Kähler metric on relatively compact domains in a complex manifold, which is the Bergman metric of the L² space of holomorphic sections of the pluricanonical bundle equipped with the Hermitian metric introduced by Narasimhan-Simha.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap91-2-5, author = {Bo-Yong Chen}, title = {A new invariant K\"ahler metric on relatively compact domains in a complex manifold}, journal = {Annales Polonici Mathematici}, volume = {92}, year = {2007}, pages = {147-159}, zbl = {1122.32008}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap91-2-5} }
Bo-Yong Chen. A new invariant Kähler metric on relatively compact domains in a complex manifold. Annales Polonici Mathematici, Tome 92 (2007) pp. 147-159. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap91-2-5/