The world viewed from outside

Journal of Geometry and Physics

Volumn 24, Issue 4, 1998, Pages 303-333

  Ozsváth, István ^a   Schücking, Engelbert L ^b  

^a UNIVERSITY OF TEXAS AT DALLAS   (United States)

^b POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Cosmology; Euclidean spaces; Stretched 3 sphere

Indexed keywords

EID: 0032016802     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(97)00015-6     Document Type: Article

References (35)

1. [1] Dante Alighieri, The Paradiso, Translated by John Ciardi, New American Library, New York (1970).
2. [2] F. Apéry, La Surface de Boy, Adv. in Math. 61 (1986).
3. [3] H. Bethe, Termaufspaltung in Kristallen, Ann. Phys. Ser. (5) 3 (1929) 133-208.
4. [4] L. Bianchi, Lezioni sulla teoria dei gruppi continui finiti di trasformationi, Spoerri, Pisa (1918).
5. [5] W. Clifford, Preliminary sketch of biquaternions, Proc. London Math. Soc. 4 (1873).
6. [6] D. DeTurckand W. Ziller, Minimal isometric immersions of spherical space forms in spheres. Comment. Math. Helvetici 67 (1992) 428-458.
7. [7] N. Ejiri, Totally real submanifolds in a 6-sphere, Proc. Amer. Math. Soc. 83 (1981) 759-763.
8. [8] K. Gödel, Rotating universes in general relativity theory, Proc. Int. Cong. Math., Vol. I (1950) 175.
9. [9] M. Gromov and V. Rohklin, Embedding and immersions in Riemannian geometry, Russian Math. Surveys 25 (1970) 1-57.
10. [10] H. Hopf, Zum Clifford-Kleinschen Raumproblem, Math. Ann. 95 (1925) 313-339.
11. [11] H. Hopf, Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche, Math. Ann. 104 (1931) 637-665.
12. [12] W. Killing, Erweiterung des Raumbegriffes, Programm Lyceum Hosianum (1884).
13. [13] F. Klein, Vorlesungen über Nicht-Euklidische Geometrie (Springer, Berlin, 1968).
14. [14] F. Klein, Lectures on the Icosahedron (Dover, New York, 1956) p.39.
15. [15] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry (Interscience, New York, 1963).
16. [16) S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 2 (Interscience, New York, 1969).
17. [17] E. Mach, The Science of Mechanics; A critical and historical account of its development, LaSalle. III. Open Court (1960).
18. [18] K. Mashimo, Minimal immersions of 3-dimensional spheres into spheres, Osaka J. Math. 2 (1984) 721-732.
19. [19] J. Nash, The Imbedding problem for Riemannian manifolds, Ann. Math. 63 (1956) 20-63.
20. [20] I. Ozsváth, An embedding problem, J. Math. Phys. 29 (1988) 825.
21. [21] I. Ozsváth, Embedding problem II, J. Math. Phys. 33 (1992) 229.
22. [22] I. Ozsváth and E. Schücking, Finite rotating Universes, Nature 193 (1962) 1168.
23. [23] I. Ozsváth and E. Schücking, Isometric embedding for homogeneous compact 3-manifolds, GRG 28 (1996) 999.
24. [24] H. Poincaré, Analysis Situs, J. de l'École Poly. (2)1 (1895) 67.
25. [25] B. Riemann, Collected Papers (New Edition by R. Narasimhan) (Springer, New York, 1990).
26. [26] M. Ryan and L. Shepley. Homogeneous Relativistic Cosmologies (Princeton University Press, Princeton. NJ, 1975).
27. [27] L. Schläfli, Nota alla memorici del Sig. Beltrami sugli spazii di curvature constante, Ann. di Matem. (2)5 (1871-1873) 170-193.
28. [28] L. Schläfli, Theorie der vielfachen Kontinuität, Denkschriften der Schweizerischen naturforschenden Gesellschaft 38 (1901) pp.i-237.
29. [29] K. Schwarzschild, Über das zulässige Krümungsmass des Raumes, Virteljahrschrift der Astronomischen Gesellschaft 35 (1900) 337.
30. [30] H. Seifert and W. Threlfall, A Textbook of Topology (Academic Press, New York, 1980).
31. [31] A. Speiser, Klassische Stücke der Mathematik, Zürich (1925).
32. [32] T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18 (1966) 380-385.
33. [33] A. Taub, Empty space-times admitting a three parameter group of motions, Ann. Math. 53 (1951) 472.
34. [34] W. Threlfall and H. Seifert, Topologische Untersuchungen der Diskontinuitäts-bereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes, I. Math. Ann. 104 (1931) 1-70; II. 107 (1932) 543-586.
35. [34] W. Threlfall and H. Seifert, Topologische Untersuchungen der Diskontinuitäts-bereiche endlicher Bewegungsgruppen des dreidimensionalen sphärischen Raumes, I. Math. Ann. 104 (1931) 1-70; II. 107 (1932) 543-586.