Locally conformally flat metrics on surfaces of general type

Mustafa Kalafat; Özgür Kelekçi

Locally conformally flat metrics on surfaces of general type

Differential Geometry 2019-01-11 v2 Geometric Topology

Authors: Mustafa Kalafat , Özgür Kelekçi

Abstract

We prove a nonexistence theorem for product type manifolds. In particular we show that the 4-manifold $\Sigma_g\times\Sigma_h$ does not admit any locally conformally flat metric arising from discrete and faithful representations for $g\geq 2$ and $h\geq 1$

Keywords

locally conformally flat metric product manifolds nonexistence theorem 4-manifold discrete faithful representations general type surfaces

Cite

@article{arxiv.1810.09020,
  title  = {Locally conformally flat metrics on surfaces of general type},
  author = {Mustafa Kalafat and Özgür Kelekçi},
  journal= {arXiv preprint arXiv:1810.09020},
  year   = {2019}
}

Comments

Important typo in the statement of the main theorem is fixed. Section 3 is modified. 11 pages

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