Ghara, SoumitraSoumitraGharaMisra, GadadharGadadharMisra2025-08-282025-08-282022-02-01http://arxiv.org/abs/2202.02402https://d8.irins.org/handle/IITG2025/20087It has been recently shown that if K is a sesqui-analytic scalar valued non-negative definite kernel on a domain ? in Cm, then the function (K2?i?�jlogK)mi,j=1, is also a non-negative definite kernel on ?. In this paper, we discuss two consequences of this result. The first one strengthens the curvature inequality for operators in the Cowen-Douglas class B1(?) while the second one gives a relationship of the reproducing kernel of a submodule of certain Hilbert modules with the curvature of the associated quotient module.en-USGaussian curvatureCowen-Douglas operatorSesqui-analytic scalarHilbert modulese-Printe-Print123456789/555