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Scalar curvature rigidity of hyperbolic product manifolds

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Abstract.

This paper presents a scalar curvature rigidity result of real hyperbolic product manifolds in analogy to M. Min–Oo’s result in [14]. In order to prove this, we consider Dirac bundles obtained from the spinor bundle, and we derive Killing equations trivializing these Dirac bundles. Moreover, an integrated Bochner–Weitzenböck formula is shown which allows the usage of the non–compact Bochner technique.

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Authors and Affiliations

  1. Mathematical Institute, University of Leipzig, D-04109, Leipzig, Germany

    Mario Listing

  2. Department of Mathematics, Stony Brook, University, Stony Brook, NY, 11794-3651, USA

    Mario Listing

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  1. Mario Listing
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Correspondence to Mario Listing.

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Mathematics Subject Classification (2000): Primary 53C24, Sec. 53C21

in final form: 11 August 2003

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Listing, M. Scalar curvature rigidity of hyperbolic product manifolds. Math. Z. 247, 581–594 (2004). https://doi.org/10.1007/s00209-003-0631-y

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  • DOI: https://doi.org/10.1007/s00209-003-0631-y

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