The Lichnerowicz Laplacian on normal homogeneous spaces

Paul Schwahn

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arXiv · 2304.10607

The Lichnerowicz Laplacian on normal homogeneous spaces

Paul Schwahn

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Abstract

We give a new formula for the Lichnerowicz Laplacian on normal homogeneous spaces in terms of Casimir operators. We derive some practical estimates and apply them to the known list of non-symmetric, compact, simply connected homogeneous spaces $G/H$ with $G$ simple whose standard metric is Einstein. This yields many new examples of Einstein metrics which are stable in the Einstein-Hilbert sense, which have long been lacking in the positive scalar curvature setting.

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Paul Schwahn. 2023-04-20. The Lichnerowicz Laplacian on normal homogeneous spaces. https://arxiv.org/abs/2304.10607

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