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arXiv · 1702.04951

Positive scalar curvature and the Euler class

Jianqing Yu·Weiping Zhang
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Abstract

We prove the following generalization of the classical Lichnerowicz vanishing theorem: if $F$ is an oriented flat vector bundle over a closed spin manifold $M$ such that $TM$ carries a metric of positive scalar curvature, then $<\widehat A(TM)e(F),[M]>=0$, where $e(F)$ is the Euler class of $F$.

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Jianqing Yu, Weiping Zhang. 2017-02-16. Positive scalar curvature and the Euler class. https://doi.org/10.1016/j.geomphys.2018.01.015

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