# The relationship of the Gaussian curvature with the curvature of a Cowen-Douglas operator

@inproceedings{Ghara2022TheRO, title={The relationship of the Gaussian curvature with the curvature of a Cowen-Douglas operator}, author={Soumitra Ghara and Gadadhar Misra}, year={2022} }

It has been recently shown that if K is a sesqui-analytic scalar valued non-negative definite kernel on a domain Ω in C, then the function ( K∂i∂̄j logK )m i,j=1 , is also a non-negative definite kernel on Ω. 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(Ω) while the second one gives a relationship of the reproducing kernel of a submodule of certain Hilbert modules with the curvature of…

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