Abstract
We prove that the image of a real analytic Riemannian manifold under a smooth Riemannian submersion is necessarily real analytic.
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I dedicate this paper to the memory of Ákos Császár, my former boss in the Department Analysis I of the Eötvös University. Hungarian mathematics and mathematicians have greatly benefited from his teachings and from his leadership during many decades. I am indebted to him for his advice and much needed help at the beginning of my own career.
Research partially supported by NSF grant DMS1764167.
The paper was written at the Rényi Institute and the Eötvös University, both of Budapest, while I was on sabbatical leave from Purdue University. I am grateful to all three institutions.
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Lempert, L. On Riemannian submersions. Acta Math. Hungar. 158, 363–372 (2019). https://doi.org/10.1007/s10474-019-00941-6
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DOI: https://doi.org/10.1007/s10474-019-00941-6