Abstract
We study singularity formation of K\(\ddot{\text {a}}\)hler–Ricci flow on a K\(\ddot{\text {a}}\)hler manifold that admits a horizontally homothetic conformal submersion into another K\(\ddot{\text {a}}\)hler manifold. We will derive necessary and sufficient conditions for the preservation of horizontally homothetic conformal submersion along the flow and establish the formation of type I singularity together with a standard splitting of the Cheeger–Gromov limit. This generalizes the setup of Calabi symmetry that was discussed in [2] and [11] and produces novel proofs for the established results.
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Acknowledgements
The author would like to express sincere gratitude to Prof. Frederick Tsz-Ho Fong for his valuable advice and support during the project.
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Hoan, N.T. K\(\ddot{\text {a}}\)hler–Ricci Flow and Conformal Submersion. Mediterr. J. Math. 20, 270 (2023). https://doi.org/10.1007/s00009-023-02472-5
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DOI: https://doi.org/10.1007/s00009-023-02472-5