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The Lichnerowicz Laplacian on normal homogeneous spaces

  • Paul Schwahn ORCID logo EMAIL logo
Published/Copyright: July 13, 2024

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 đș 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.

Acknowledgements

The author is indebted to Prof. G. Weingart for the spark of inspiration that led to the exact formula for Δ L in terms of Casimir operators, to Prof. E. Lauret for introducing him to the versatile software system SageMath, and to Prof. U. Semmelmann for many enlightening discussions.

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Received: 2023-10-05
Revised: 2024-05-03
Published Online: 2024-07-13
Published in Print: 2024-09-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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