Mathematische Annalen

, Volume 319, Issue 4, pp 675–706 | Cite as

Total excess on length surfaces

  • Yoshiroh Machigashira
  • Fumiko Ohtsuka
Original article


We study the space of directions on a length space and examine examples having particular spaces of directions. Then we generalize the notion of total excess on length spaces satisfying some suitable conditions, which we call good surfaces. For good surfaces we generalize the Euler characteristic, and prove the generalized Gauss-Bonnet Theorem and other relations between the total excess and the Euler characteristic. Furthermore, we see that the Gaussian curvature can be defined almost everywhere on a good surface with non-positive total excess.

Mathematics Subject Classification (1991): 53C23, 53C70 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Yoshiroh Machigashira
    • 1
  • Fumiko Ohtsuka
    • 2
  1. 1.Division of Mathematical Sciences, Osaka Kyoiku University, Kashiwara-shi, Osaka 582-8582, Japan (e-mail: JP
  2. 2.Department of Mathematical Science, Faculty of Science, Ibaraki University, Mito 310-8512, Japan (e-mail: JP

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