×

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
PDFBibTeX XMLCite
Full Text: DOI

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. · JFM 29.0522.01
[6] J. Milnor, Morse theory, Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51, Princeton University Press, Princeton, N.J., 1963. · Zbl 0108.10401
[7] S. B. Myers, Riemannian manifolds with positive mean curvature, Duke Math. J. 8 (1941), 401 – 404. · Zbl 0025.22704
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.