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Extended Abstracts Fall 2013 pp 57–59Cite as

Birkhäuser

Total Curvature of Complete Surfaces in Hyperbolic Space

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

Abstract

We present a Gauss–Bonnet type formula for complete surfaces in n-dimensional hyperbolic space \(\mathbb{H}^{n}\) under some assumptions on their asymptotic behaviour. As in recent results for Euclidean submanifolds (see Dillen–Kühnel [4] and Dutertre [5]), the formula involves an ideal defect, i.e., a term involving the geometry of the set of points at infinity.

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References

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  5. N. Dutertre, A Gauss–Bonnet formula for closed semi-algebraic sets. Adv. Geom. 8, 33–51 (2008)

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Author information

Authors and Affiliations

  1. Tokyo Metropolitan University, Tokyo, Japan

    Jun O’Hara

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

    Gil Solanes

Authors
  1. Jun O’Hara
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  2. Gil Solanes
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Corresponding author

Correspondence to Jun O’Hara .

Editor information

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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O’Hara, J., Solanes, G. (2015). Total Curvature of Complete Surfaces in Hyperbolic Space. 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_11

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