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arXiv · 2207.00645

Global obstructions to conformally Einstein metrics in dimension six

Jeffrey S. Case
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Abstract

We present a global conformal invariant on closed six-manifolds which obstructs the existence of a conformally Einstein metric. We show that this obstruction is nontrivial and, up to multiplication by a constant, is the unique such invariant. This also gives rise to a (possibly trivial) diffeomorphism invariant which obstructs the existence of an Einstein metric. We also discuss global conformal invariants which obstruct the existence of a conformally Einstein metric on closed six-manifolds with infinite fundamental group.

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Jeffrey S. Case. 2022-07-01. Global obstructions to conformally Einstein metrics in dimension six. https://arxiv.org/abs/2207.00645

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