Volume 18, issue 3 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 9, 4731–5219
Issue 8, 4139–4730
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Germs of fibrations of spheres by great circles always extend to the whole sphere

Patricia Cahn, Herman Gluck and Haggai Nuchi

Algebraic & Geometric Topology 18 (2018) 1323–1360
Bibliography
1 M Berger, Blaschke’s conjecture for spheres236 MR496885
2 W Blaschke, Vorlesungen über Differentialgeometrie, I, 1, Springer (1921)
3 P Cahn, H Gluck, H Nuchi, Deformation and extension of fibrations of spheres by great circles, (2015) arXiv:1502.03428
4 J Eells Jr., N H Kuiper, Manifolds which are like projective planes, Inst. Hautes Études Sci. Publ. Math. 14 (1962) 5 MR0145544
5 A Galántai, C J Hegedűs, Jordan’s principal angles in complex vector spaces, Numer. Linear Algebra Appl. 13 (2006) 589 MR2253294
6 H Gluck, Higher curvatures of curves in euclidean space, II, Amer. Math. Monthly 74 (1967) 1049 MR0227873
7 H Gluck, F W Warner, Great circle fibrations of the three-sphere, Duke Math. J. 50 (1983) 107 MR700132
8 H Gluck, F Warner, C T Yang, Division algebras, fibrations of spheres by great spheres and the topological determination of space by the gross behavior of its geodesics, Duke Math. J. 50 (1983) 1041 MR726317
9 L W Green, Auf Wiedersehensflächen, Ann. of Math. 78 (1963) 289 MR0155271
10 M Harrison, Skew flat fibrations, Math. Z. 282 (2016) 203 MR3448380
11 H Hopf, Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche, Math. Ann. 104 (1931) 637 MR1512691
12 H Hopf, Über die Abbildungen von Sphären auf Sphären niedrigerer Dimension, Fund. Math. 25 (1935) 427
13 C Jordan, Essai sur la géométrie à n dimensions, Bull. Soc. Math. France 3 (1875) 103 MR1503705
14 J Kazdan, An inequality arising in geometry MR496885
15 B McKay, The Blaschke conjecture and great circle fibrations of spheres, Amer. J. Math. 126 (2004) 1155 MR2089085
16 B McKay, Summary of progress on the Blaschke conjecture, (2013) arXiv:1309.1326
17 J Milnor, On manifolds homeomorphic to the 7–sphere, Ann. of Math. 64 (1956) 399 MR0082103
18 H Nakagawa, K Shiohama, On Riemannian manifolds with certain cut loci, Tôhoku Math. J. 22 (1970) 14 MR0261495
19 H Nakagawa, K Shiohama, On Riemannian manifolds with certain cut loci, II, Tôhoku Math. J. 22 (1970) 357 MR0278233
20 H Omori, A class of Riemannian metrics on a manifold, J. Differential Geometry 2 (1968) 233 MR0239625
21 M Salvai, On the geometry of the space of oriented lines of Euclidean space, Manuscripta Math. 118 (2005) 181 MR2177684
22 M Salvai, Global smooth fibrations of 3 by oriented lines, Bull. Lond. Math. Soc. 41 (2009) 155 MR2482001
23 K Scharnhorst, Angles in complex vector spaces, Acta Appl. Math. 69 (2001) 95 MR1868915
24 N Steenrod, The topology of fibre bundles, 14, Princeton Univ. Press (1951) MR0039258
25 A Weinstein, On the volume of manifolds all of whose geodesics are closed, J. Differential Geometry 9 (1974) 513 MR0390968
26 C T Yang, Odd-dimensional wiedersehen manifolds are spheres, J. Differential Geom. 15 (1980) 91 MR602442
27 C T Yang, Smooth great circle fibrations and an application to the topological Blaschke conjecture, Trans. Amer. Math. Soc. 320 (1990) 507 MR1028766