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Monotonicity for the Chern-Moser-Weyl curvature tensor and CR embeddings

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Abstract

We give, in this paper, a monotonicity formula for the Chern-Moser-Weyl curvature tensor under the action of holomorphic embeddings between Levi non-degenerate hypersurfaces with the same positive signature. As an application, we provide some concrete examples of algebraic Levi non-degenerate hypersurfaces with positive signature that are not embeddable into a hyperquadric of the same signature in a complex space of higher dimension.

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References

  1. Forstneric F. Embedding strictly pseudoconvex domains into balls. Trans Amer Math Soc, 295(1): 347–368 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  2. Zaitsev D. Obstructions to embeddability into hyperquadrics and explicit examples. Math Ann, 342(3): 695–726 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Webster S M. Some birational invariants for algebraic real hypersurfaces. Duke Math J, 45(1): 39–46 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  4. Griffths P, Harris J. Principles of Algebraic Geometry. New York: Wiley, 1978

    Google Scholar 

  5. Yau S T. A general Schwarz lemma for Kähler manifolds. Amer J Math, 100: 197–203 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chern S S, Moser J K. Real hypersurfaces in complex manifolds. Acta Math, 133: 219–271 (1974)

    Article  MathSciNet  Google Scholar 

  7. Webster S M. Pseudo-Hermitian structures on a real hypersurface. J Diff Geom, 13: 25–41 (1978)

    MATH  MathSciNet  Google Scholar 

  8. Stein E, Weiss G. Introduction to Fourier Analysis on Euclidean Spaces. Princeton: Princeton University Press, 1971

    MATH  Google Scholar 

  9. Baouendi M S, Huang X. Super-rigidity for holomorphic mappings between hyperquadrics with positive signature. J Diff Geom, 69: 379–398 (2005)

    MATH  MathSciNet  Google Scholar 

  10. Huang X. On a linearity problem of proper holomorphic mappings between balls in complex spaces of different dimensions. J Diff Geom, 51: 13–33 (1999)

    MATH  Google Scholar 

  11. Baouendi S, Ebenfelt P, Rothschild L. Transversality of holomorphic mappings between real hypersurfaces in different dimensions. Comm Anal Geom, 15(3): 589–611 (2007)

    MATH  MathSciNet  Google Scholar 

  12. Ebenfelt P, Huang X, Zaitsev D. The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics. Amer J Math, 127: 169–191 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Forstneric F. Most real analytic Cauchy-Riemann manifolds are nonalgebraizable, Manuscripta Math, 115: 489–494 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08903, USA

    XiaoJun Huang

  2. Department of Mathematics, University of California at San Diego, La Jolla, CA, 92093, USA

    Yuan Zhang

Authors
  1. XiaoJun Huang
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  2. Yuan Zhang
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Corresponding author

Correspondence to XiaoJun Huang.

Additional information

Dedicated to Professor ZHONG TongDe on the occasion of his 80th birthday

This work was supported by National Science Foundation (Grant No. 0801056)

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Huang, X., Zhang, Y. Monotonicity for the Chern-Moser-Weyl curvature tensor and CR embeddings. Sci. China Ser. A-Math. 52, 2617–2627 (2009). https://doi.org/10.1007/s11425-009-0204-6

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  • DOI: https://doi.org/10.1007/s11425-009-0204-6

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