| Title:
|
Lorentzian geometry as determined by the volumes of small truncated light cones (English) |
| Author:
|
Schimming, Rainer |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
24 |
| Issue:
|
1 |
| Year:
|
1988 |
| Pages:
|
5-15 |
| . |
| Category:
|
math |
| . |
| MSC:
|
53B30 |
| idZBL:
|
Zbl 0662.53020 |
| idMR:
|
MR983003 |
| . |
| Date available:
|
2008-06-06T06:18:17Z |
| Last updated:
|
2012-05-09 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107304 |
| . |
| Reference:
|
[1] B.-Y. Chen, L. Vanhecke: Total curvatures of geodesic spheres.Archiv d. Math. 32 (1979), 404-411. Zbl 0416.53025, MR 0545165 |
| Reference:
|
[2] B.-Y. Chen, L. Vanhecke: Differential geometry of geodesic spheres.J. f. d. reine u. angew. Math. 325 (1981), 28-67. Zbl 0503.53013, MR 0618545 |
| Reference:
|
[3] R. Courant, D. Hilbert: Methods of Mathematical Physics.Vol. 2, Interscience, New York, 1977. |
| Reference:
|
[4] F. Gackstatter, B. Gackstatter: Über Volumendefekte und Krümmung in Riemannschen Mannigfaltigkeiten mit Anwendungen in der Relativitätstheorie.Annalen d. Physik (7) 41 (1984), 35-44. Zbl 0551.53037, MR 0780988 |
| Reference:
|
[5] A. Gray: The volume of a small geodesic ball of a Riemannian manifold.Michigan Math. J. 20 (1973), 329-344. Zbl 0279.58003, MR 0339002 |
| Reference:
|
[6] A. Gray: Geodesic balls in Riemannian product manifolds.in: M. Cahen and M. Flato (eds.), Differential Geometry and Relativity, Reidel, Dordrecht, 1976. Zbl 0345.53007, MR 0438252 |
| Reference:
|
[7] A. Gray, L. Vanhecke: Riemannian geometry as determined by the volumes of small geodesic balls.Acta math. 142 (1979), 157-198. Zbl 0428.53017, MR 0521460 |
| Reference:
|
[8] P. Günther: Einige Sätze über das Volumenelement eines Riemannschen Raumes.Publ. Math. Debrecen 7 (1960), 78-93. MR 0141058 |
| Reference:
|
[9] O. Kowalski: Additive volume invariants of Riemannian manifolds.Acta math. 145 (1980), 205-225. Zbl 0454.53031, MR 0590290 |
| Reference:
|
[10] O. Kowalski: The volume conjecture and four-dimensional hypersurfaces.Comment. Math. Univers. Carol. 23 (1982), 81-87. Zbl 0489.53050, MR 0653352 |
| Reference:
|
[11] O. Kowalski, L. Vanhecke: Ball-homogeneous and disk-homogeneous Riemannian manifolds.Math. Z. 180 (1982), 429-444. Zbl 0476.53023, MR 0666999 |
| Reference:
|
[12] O. Kowalski, L. Vanhecke: On disk-homogeneous symmetric spaces.Ann. Glob. Analysis and Geom. 1 (1983), 91-104. Zbl 0533.53047, MR 0739899 |
| Reference:
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[13] O. Kowalski, L. Vanhecke: The volume of geodesic disks in a Riemannian manifold.Czech. Math. J. 35 (1985), 66-77. Zbl 0586.53006, MR 0779337 |
| Reference:
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[14] O. Kowalski, L. Vanhecke: Two-point functions on Riemannian manifolds.Ann. Glob. Analysis and Geom. 3 (1985), 95-119. Zbl 0571.53031, MR 0812315 |
| Reference:
|
[15] A. Lichnerowicz, A. G. Walker: Sur les espaces riemanniens harmoniques de type hyperbolique normal.C. R. Acad. Sc. Paris 221 (1945), 394-396. Zbl 0060.38507, MR 0015269 |
| Reference:
|
[16] V. Miquel: The volumes of small geodesic balls for a metric connection.Compositio Math. 46 (1982), 121-132. Zbl 0489.53043, MR 0660156 |
| Reference:
|
[17] V. Miquel: Volumes of certain small geodesic balls and almost Hermitean geometry.Geometriae Dedicata 15 (1984), 261 -267. MR 0739929 |
| Reference:
|
[18] H. S. Ruse A. G. Walker, and T. J. Willmore: Harmonic Spaces.Edizioni Cremonese, Roma, 1961. MR 0142062 |
| Reference:
|
[19] R. Schimming: Riemannian manifolds for which a power of the radius is k-harmonic.Z. f. Analysis u. ihre Anw. 4 (1985), 235-249. Zbl 0571.53012, MR 0807133 |
| . |
