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Constant Scalar Curvature Metrics on Hirzebruch Surfaces

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Extended Abstracts Fall 2013

Part of the book series: Trends in Mathematics ((RPCRMB))

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Abstract

For each natural number m ≥ 0, a complex surface \(\Sigma _{m}\) called Hirzebruch surface is defined in [8].

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Notes

  1. 1.

    We note that in the fourth dimension, a constant scalar curvature metric g is stable with respect to the Yamabe functional if and only if its scalar curvature R and the first eigenvalue \(\lambda _{1}\) of its Laplacian \(\Delta = -\text{trace }\nabla ^{2}\) satisfy the inequality \(\lambda _{1} \geq R/3\), see [11].

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Author information

Authors and Affiliations

  1. Graduate School of Science and Technology, Keio University, Yokohama, Japan

    Nobuhiko Otoba

Authors
  1. Nobuhiko Otoba
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Correspondence to Nobuhiko Otoba .

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Editors and Affiliations

  1. Departament de Matemàtica Aplicada, Universitat Politècnica de Catalunya, Barcelona, Spain

    Maria del Mar González

  2. Department of Mathematics, Princeton University, Princeton, New Jersey, USA

    Paul C. Yang

  3. School of Mathematics, University of Leeds, Leeds, United Kingdom

    Nicola Gambino

  4. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Barcelona, Spain

    Joachim Kock

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Otoba, N. (2015). Constant Scalar Curvature Metrics on Hirzebruch Surfaces. In: González, M., Yang, P., Gambino, N., Kock, J. (eds) Extended Abstracts Fall 2013. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-21284-5_12

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