Curvature Functionals on Spaces of Associated Metrics
In this chapter we discuss a number of curvature functionals defined on the spaces of associated metrics for both compact symplectic and compact contact manifolds. Since these spaces are smaller than the space of Riemannian metrics of the same total volume, one expects for the classical curvature functionals weaker but still interesting critical point conditions. Other functionals that depend on the symplectic and contact structures are also considered.
KeywordsScalar Curvature Ahler Manifold Riemannian Metrics Contact Manifold Ricci Operator
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