A Proof of the Gauss - Bonnet Theorem
Keywords:
Gauss – Bonnet theorem, Gaussian surface curvature
Abstract
The paper proposes a new proof of the well-known Gauss-Bonnet theorem, based only on metric considerations. The theorem is first proved for triangles lying in the injectivity domain of the exponential mapping, and then, using standard techniques, it is extended to arbitrary domains
References
A. V. Pogorelov. Differential geometry. M., "Science",1969.
Milnor J. Morse Theory. M., "Mir",1965.
Alexandrov A.D. and Zalgaller V.A. Two-dimensional manifolds of bounded curvature. Tr. MIAN USSR, V.LXIII, 1962.
Akbarov S.A. and Toponogov V.A. A comparison theorem for the angles of a triangle for a class of Riemannian manifolds. Proceedings of the Institute of Mathematics, Academy of Sciences of the USSR Sib. Branch, 1987. Т. 9.p. 16-25.
Milnor J. Morse Theory. M., "Mir",1965.
Alexandrov A.D. and Zalgaller V.A. Two-dimensional manifolds of bounded curvature. Tr. MIAN USSR, V.LXIII, 1962.
Akbarov S.A. and Toponogov V.A. A comparison theorem for the angles of a triangle for a class of Riemannian manifolds. Proceedings of the Institute of Mathematics, Academy of Sciences of the USSR Sib. Branch, 1987. Т. 9.p. 16-25.
Published
2021-03-19
How to Cite
Akbarov Sayitali Askarovich. (2021). A Proof of the Gauss - Bonnet Theorem. CENTRAL ASIAN JOURNAL OF MATHEMATICAL THEORY AND COMPUTER SCIENCES, 2(3), 23-26. Retrieved from https://cajmtcs.centralasianstudies.org/index.php/CAJMTCS/article/view/66
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