Prescribing Integral Curvature Equation
نویسنده
چکیده
In this paper we formulate new curvature functions on Sn via integral operators. For certain even orders, these curvature functions are equivalent to the classic curvature functions defined via differential operators, but not for all even orders. Existence result for antipodally symmetric prescribed curvature functions on Sn is obtained. As a corollary, the existence of a conformal metric for an antipodally symmetric prescribed Q−curvature functions on S3 is proved. Curvature function on general compact manifold as well as the conformal covariance property for the corresponding integral operator are also addressed. 1. Formulation of the problem and the main results The main problem we will consider in this paper is the solvability of the following integral equation:
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