Historia twierdzenia Gaussa-Bonneta i socjologia matematyki

• Autorzy: Gottlieb D.H.
• Języki publikacji: PL

Słowa kluczowe

PL

historia matematyki; liczba Eulera-Poincarégo; stopień odwzorowania

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Wiadomości Matematyczne
• Rocznik: 2010
• Tom: T. 46, Nr 1
• Strony: 63--80
• Opis fizyczny: Bibliogr. 25 poz., wykr.

Twórcy

autor

Gottlieb D.H.

• Department of Mathematics Purdue University,

Bibliografia

• [1] C. B. Allendoerfer, The Euler Number of a Riemannian manifold, Amer. J. Math. 62 (1940), 243-248.
• [2] G. E. Bredon, Topology and Geometry, Graduate Text in Mathematics, New York, 1993.
• [3] G. E. Bredon, A. Kosinski, Vector fields on _-manifolds, Annals of Math. 84 (1966), 85-90.
• [4] S. S. Chern, A simple intrinsic proof of the Gauss-Bonnet theorem for closed Riemannian manifolds, Annals of Math. 45 (1944), 747-752.
• [5] W. Fenchel, On the total curvature of Riemannian manifolds, I, J. London Math. Soc. 15 (1940), 15-22.
• [6] D. H. Gottlieb, On the index of pullback vector fields, Lecture Notes in Mathematics, vol. 1350, Springer-Verlag, 1987.
• [7] D. H. Gottlieb, Zeroes of pullback vector fields and fixed point theory for bodies, Contemporary Mathematics 96 (1989), 163-179.
• [8] A. Gray, Tubes, Addison-Wesley, Redwood City California, 1990.
• [9] D. H. Gottlieb, G. Samaranayake, Index of discontinuous vector fields, New York J. Math. 1 (1994/95), 130-148.
• [10] B. Grünbaum, G. C. Shephard, A new look at Euler's Theorem for polyhedra, Amer. Math. Monthly 101 (1994), 109-128.
• [11] A. Haefliger, Quelques remarques sur les applications differentiables d'une surface dans le plan, Ann. Inst. Fourier 10 (1960), 47-60.
• [12] P. J. Hilton, J. Pederson, Euler's Theorem for polyhedra: A Topologist and a Geometer respond, Amer. Math. Monthly 101 (1994), 959-962.
• [13] M. W. Hirsch, Differential Topology, Springer-Verlag, New York, 1976.
• [14] H. Hopf, ¨ Uber die Curvatura integra geschlossener Hyperflächen, Math. Ann. 95 (1925), 340-376.
• [15] H. Hopf, Vektorfelder in n-dimensionalen Mannigfaltigkeiten, Math. Ann. 96 (1927), 225-250.
• [16] H. Hopf, Differential Geometrie und Topological Gestalt, Jahresbericht der Deutcher Math. Verein. 41 (1932), 209-229.
• [17] H. Hopf, Differential Geometry in the Large: Seminar Lectures NYU 1946 and Stanford 1956, Lecture Notes in Mathematics, vol. 1000, Springer Verlag, 1983.
• [18] M. E. Kervaire, Courbure integrale generalisee et homotopie, Math. Ann. 131 (1956), 219-252.
• [19] I. Lakatos, Proofs and Refutations: The Logic of Mathematical Discovery, Cambridge University Press, Cambridge, 1976.
• [20] J. W. Milnor, On the immersion of n-manifolds in (n + 1)-dimensional space, Commentarii Math. Helvetici 30 (1956), 275-284.
• [21] M. Morse, Singular points of vector fields under general boundary conditions, Amer. J. Math 51 (1929), 165-178.
• [22] H. Samelson, On immersion of manifolds, Canadian J. Math. 12 (1960), 529-534.
• [23] H. Samelson, Descartes and Differential Geometry, in: Geometry, Topology, and Physics for Raoul Bott (S. T. Yau, ed.), International Press, Boston, 1995.
• [24] J. Stillwell, Mathematics and its History, Springer-Verlag, New York, 1974.
• [25] M. Spivak, A Comprehensive Introduction to Differential Geometry, 2nd ed., vol. 1-5, Publish or Perish, Houston, 1979.