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On Riemannian submersions

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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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References

  1. Aguilar, R.: Symplectic reduction and the homogenous complex Monge-Ampère equation. Ann. Global Anal. Geom. 19, 327–353 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. V. Guillemin and M. Stenzel, Grauert tubes and the homogeneous Monge–Ampère equation. I, J. Diff. Geom., 34 (1991), 561–570

  3. Hill, C.D., Taylor, M.: Integrability of rough almost complex structures. J. Geom. Anal. 13, 163–172 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. L. Lempert, Complex structures on the tangent bundle of Riemannian manifolds, in: Complex Analysis and Geometry, V. Ancona and A. Silva, eds., Plenum Press (New York, 1992), pp. 235–251

  5. L. Lempert, Adapted complex and involutive structures, arxiv:1901.03388.

  6. Lempert, L., Szőke, R.: Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundles of Riemannian manifolds. Math. Ann. 290, 689–712 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lempert, L., Szőke, R.: A new look at adapted complex structures. Bull. London Math. Soc. 44, 367–374 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Newlander and L. Nirenberg, Complex coordinates in almost complex manifolds, Ann. of Math. (2), 65 (1957), 391–404

  9. O'Neill, B.: Semi-Riemannian Geometry. Academic Press (New York, With Applications to Relativity (1983)

    MATH  Google Scholar 

  10. Szőke, R.: Complex structures on the tangent bundles of Riemannian manifolds. Math. Ann. 291, 409–428 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  11. Szőke, R.: Automorphisms of certain Stein manifolds. Math. Z. 219, 357–385 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  12. Szőke, R.: Canonical complex structures associated to connections and the complexification of Lie groups. Math. Ann. 329, 553–591 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907-2067, USA

    L. Lempert

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  1. L. Lempert
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Correspondence to L. Lempert.

Additional information

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

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