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arXiv · 2309.05544

Sasakian Geometry on Sphere Bundles II: Constant Scalar Curvature

Charles P. Boyer·Christina W. Tønnesen-Friedman
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Abstract

In a previous paper [BTF21] the authors employed the fiber join construction of Yamazaki [Yam99] together with the admissible construction of Apostolov, Calderbank, Gauduchon, and T{\o}nnesen-Friedman [ACGTF08a] to construct new extremal Sasaki metrics on odd dimensional sphere bundles over smooth projective algebraic varieties. In the present paper we continue this study by applying a recent existence theorem [BHLTF23] that shows that under certain conditions one can always obtain a constant scalar curvature Sasaki metric in the Sasaki cone. Moreover, we explicitly describe this construction for certain sphere bundles of dimension 5 and 7.

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Charles P. Boyer, Christina W. Tønnesen-Friedman. 2023-09-11. Sasakian Geometry on Sphere Bundles II: Constant Scalar Curvature. https://arxiv.org/abs/2309.05544

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