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Geodesics in piecewise linear manifolds. (English) Zbl 0328.53033


MSC:

53C20 Global Riemannian geometry, including pinching
53C70 Direct methods (\(G\)-spaces of Busemann, etc.)
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
57Q99 PL-topology
57R70 Critical points and critical submanifolds in differential topology
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References:

[1] A. D. Aleksandrov and V. A. Zalgaller, Two-dimensional manifolds of bounded curvature. (Foundations of the intrinsic geometry of surfaces.), Trudy Mat. Inst. Steklov. 63 (1962), 262 (Russian). · Zbl 0122.17005
[2] Thomas Banchoff, Critical points and curvature for embedded polyhedra, J. Differential Geometry 1 (1967), 245 – 256. · Zbl 0164.22903
[3] É. Cartan, Leçons sur la géométrie des espaces de Riemann, 2ième éd., Gauthier-Villars, Paris, 1926, 1946. MR 8, 602. · Zbl 0044.18401
[4] H. R. Gluck, Piecewise linear methods in Riemannian geometry, Univ. of Pennsylvania, 1972 (mimeographed notes).
[5] J. Hadamard, Les surfaces à courbures opposées, J. Math. Pures Appl. (5) 4 (1898), 27-73.
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[8] Howard Osborn, Function algebras and the de Rham theorem in \?\?, Bull. Amer. Math. Soc. 77 (1971), 386 – 391. · Zbl 0214.48903
[9] Alexandre Preissman, Quelques propriétés globales des espaces de Riemann, Comment. Math. Helv. 15 (1943), 175 – 216 (French). · Zbl 0027.25903 · doi:10.1007/BF02565638
[10] Willi Rinow, Die innere Geometrie der metrischen Räume, Die Grundlehren der mathematischen Wissenschaften, Bd. 105, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. · Zbl 0096.16302
[11] C. P. Rourke and B. J. Sanderson, Introduction to piecewise-linear topology, Springer-Verlag, New York-Heidelberg, 1972. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 69. · Zbl 0254.57010
[12] John Stallings, The piecewise-linear structure of Euclidean space, Proc. Cambridge Philos. Soc. 58 (1962), 481 – 488. · Zbl 0107.40203
[13] David A. Stone, Sectional curvature in piecewise linear manifolds, Bull. Amer. Math. Soc. 79 (1973), 1060 – 1063. · Zbl 0273.53054
[14] J. L. Synge, On the connectivity of spaces of positive curvature, Quart. J. Math. 7 (1936), 316-320. · Zbl 0015.41601
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