Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Scalar curvature estimates by parallel alternating torsion

Author: Sebastian Goette
Journal: Trans. Amer. Math. Soc. 363 (2011), 165-183
MSC (2010): Primary 53C21; Secondary 58J20, 53C15, 53C30
Published electronically: August 20, 2010
MathSciNet review: 2719677
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Abstract: We generalize Llarull's scalar curvature comparison to Riemannian manifolds admitting metric connections with parallel and alternating torsion and having a nonnegative curvature operator on  $ \Lambda^2TM$. As a by-product, we show that the Euler number and signature of such manifolds are determined by their global holonomy representation. Our result holds in particular for all quotients of compact Lie groups of equal rank, equipped with a normal homogeneous metric.

We also correct a mistake in the treatment of odd-dimensional spaces in our earlier papers.

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Sebastian Goette
Affiliation: Mathematisches Institut, Universität Freiburg, Eckerstr. 1, 79104 Freiburg, Germany

Keywords: Scalar curvature, skew torsion, parallel torsion, homogeneous spaces
Received by editor(s): October 10, 2007
Received by editor(s) in revised form: July 25, 2008
Published electronically: August 20, 2010
Additional Notes: This research was supported in part by DFG special programme “Global Differential Geometry”
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.