Hidden Symmetries of Euclideanised Kerr-NUT-(A)dS Metrics in Certain Scaling Limits
Mihai Visinescu, Gabriel Eduard Vilcu
TL;DR
This paper explores hidden symmetries in higher-dimensional Kerr-NUT-(A)dS metrics, revealing their connections to Einstein-Sasaki spaces and identifying new Killing forms through geometric analysis.
Contribution
It uncovers the complete set of Killing-Yano tensors for Einstein-Sasaki spaces and introduces two novel Killing forms linked to the cone's complex volume form.
Findings
Complete set of Killing-Yano tensors for Einstein-Sasaki spaces
Identification of two new Killing forms on Einstein-Sasaki manifolds
Analysis of Killing forms on mixed 3-Sasaki manifolds
Abstract
The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new Killing forms on Einstein-Sasaki manifolds are identified associated with the complex volume form of the cone manifolds. Finally the Killing forms on mixed 3-Sasaki manifolds are briefly described.
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