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A Cubic Form Differential Inequality with Applications to Affine Kähler–Ricci Flat Manifolds

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Abstract.

In this paper we derive an differential inequality for the Laplacian ΔJ of the relative Pick invariant J. As application we generalize the following result of E. Calabi: every affine complete, parabolic affine hypersphere is an elliptic paraboloid.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan Prov., 610064, People’s Republic China

    An-Min Li

  2. College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan Prov., 453007, People’s Republic China

    Ruiwei Xu

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  1. An-Min Li
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  2. Ruiwei Xu
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Correspondence to An-Min Li.

Additional information

The first author is partially supported by NKBRPC(2006CB805905), NSFC 10631050 and RFDP.

Received: April 27, 2008. Revised: November 3, 2008. Accepted: November 17, 2008.

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Li, AM., Xu, R. A Cubic Form Differential Inequality with Applications to Affine Kähler–Ricci Flat Manifolds. Results. Math. 54, 329–340 (2009). https://doi.org/10.1007/s00025-009-0366-0

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  • DOI: https://doi.org/10.1007/s00025-009-0366-0

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