Moduli spaces of oriented Type $\mathcal{A}$ manifolds of dimension at least 3

Peter Gilkey; JeongHyeong Park

doi:10.4134/JKMS.j160647

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J. Korean Math. Soc. 2017; 54(6): 1759-1786

Online first article May 29, 2017 Printed November 1, 2017

https://doi.org/10.4134/JKMS.j160647

Moduli spaces of oriented Type $\mathcal{A}$ manifolds of dimension at least 3

Peter Gilkey, JeongHyeong Park

University of Oregon, Sungkyunkwan University

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Abstract

We examine the moduli space of oriented locally homogeneous manifolds of Type~$\mathcal{A}$ which have non-degenerate symmetric Ricci tensor both in the setting of manifolds with torsion and also in the torsion free setting where the dimension is at least 3. These exhibit phenomena that is very different than in the case of surfaces. In dimension 3, we determine all the possible symmetry groups in the torsion free setting.

Keywords: Ricci tensor, moduli space, homogeneous affine manifold

MSC numbers: 53C21