@article{oai:u-ryukyu.repo.nii.ac.jp:02006999,
author = {Kamiyama, Yasuhiko and 神山, 靖彦},
journal = {Ryukyu mathematical journal},
month = {Dec},
note = {If X, a compact connected closed C^∞-surface with Euler-Poincaré characteristic _X(X), has a Riemannian metric, and if K : X → R is the Gauss-curvature and dV is the absolute value of the exterior 2-form which represents the volume, then according to the theorem of Gauss-Bonnet, which holds for orientable as well as non-orientable surfaces, (2π)/1 ∫_xKdV=_X(X). When X is the standard sphere or torus in R^3 , the Gaussian curvature is well-known and we can compute the left-hand side explicitly. Let X be a compact connected closed C^∞-surface of any genus. In this paper, we construct an embedding of X into R^3 or R^4 according as X is orientable or nonorientable. We equip X with the Riemannian metric as a Riemannian submanifold of R^3 or R^4. Then, with the aid of a computer, we compute the left-hand side numerically for the cases that the genus of X is small. The computer data are sufficiently nice and coincide with the right-hand side without errors. Such nice data are obtained by converting double integrals to infinite integrals., 紀要論文},
pages = {1--17},
title = {COMPUTER-AIDED VERIFICATION OF THE GAUSS-BONNET FORMULA FOR CLOSED SURFACES},
volume = {24},
year = {2011}
}