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Decomposition of closed orientable geometric surfaces into acute geodesic triangles

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Abstract

We prove that for every \(g\ge 2\), a differentiable closed orientable geometric surface of genus g may be decomposed into \(16g-16\) acute geodesic triangles. We also determine the number of acute geodesic triangles needed for the sphere and the torus.

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Authors and Affiliations

  1. School of Mathematics, Statistics and Computer Science, University of Kwazulu Natal, Private Bag X01, Scottsville, Pietermaritzburg, South Africa

    Sheng Bau

  2. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Stephen M. Gagola III

Authors
  1. Sheng Bau
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  2. Stephen M. Gagola III
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Corresponding author

Correspondence to Stephen M. Gagola III.

Additional information

The work of this paper was supported by NRF Competitive Grant No.: CPRR/93507, 2015.

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Bau, S., Gagola, S.M. Decomposition of closed orientable geometric surfaces into acute geodesic triangles. Arch. Math. 110, 81–89 (2018). https://doi.org/10.1007/s00013-017-1097-1

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  • DOI: https://doi.org/10.1007/s00013-017-1097-1

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