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arXiv · 1501.06784

On the Yamabe Problem on contact Riemannian Manifolds

Feifan Wu·Wei Wang
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Abstract

Contact Riemannian manifolds, whose complex structures are not necessarily integrable, are generalization of pseudohermitian manifolds in CR geometry. The Tanaka-Webster-Tanno connection plays the role of the Tanaka-Webster connection of a pseudohermitian manifold. Conformal transformations and the Yamabe problem are also defined naturally in this setting. By constructing the special frames and the normal coordinates on a contact Riemannian manifold, we prove that if the complex structure is not integrable, its Yamabe invariant on a contact Riemannian manifold is always less than the Yamabe invariant of the Heisenberg group. So the Yamabe problem on a contact Riemannian manifold is always solvable.

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Feifan Wu, Wei Wang. 2015-01-27. On the Yamabe Problem on contact Riemannian Manifolds. https://arxiv.org/abs/1501.06784

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