Lorentzian geometry as determined by the volumes of small truncated light cones

Rainer Schimming

Archivum Mathematicum (1988)

  • Volume: 024, Issue: 1, page 5-15
  • ISSN: 0044-8753

How to cite

top

Schimming, Rainer. "Lorentzian geometry as determined by the volumes of small truncated light cones." Archivum Mathematicum 024.1 (1988): 5-15. <http://eudml.org/doc/18228>.

@article{Schimming1988,
author = {Schimming, Rainer},
journal = {Archivum Mathematicum},
keywords = {Lorentzian manifold; truncated light cone; volume; flat; Ricci-flat},
language = {eng},
number = {1},
pages = {5-15},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Lorentzian geometry as determined by the volumes of small truncated light cones},
url = {http://eudml.org/doc/18228},
volume = {024},
year = {1988},
}

TY - JOUR
AU - Schimming, Rainer
TI - Lorentzian geometry as determined by the volumes of small truncated light cones
JO - Archivum Mathematicum
PY - 1988
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 024
IS - 1
SP - 5
EP - 15
LA - eng
KW - Lorentzian manifold; truncated light cone; volume; flat; Ricci-flat
UR - http://eudml.org/doc/18228
ER -

References

top
  1. B.-Y. Chen, L. Vanhecke, Total curvatures of geodesic spheres, Archiv d. Math. 32 (1979), 404-411. (1979) Zbl0416.53025MR0545165
  2. B.-Y. Chen, L. Vanhecke, Differential geometry of geodesic spheres, J. f. d. reine u. angew. Math. 325 (1981), 28-67. (1981) Zbl0503.53013MR0618545
  3. R. Courant, D. Hilbert, Methods of Mathematical Physics, Vol. 2, Interscience, New York, 1977. (1977) 
  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. (1984) Zbl0551.53037MR0780988
  5. A. Gray, The volume of a small geodesic ball of a Riemannian manifold, Michigan Math. J. 20 (1973), 329-344. (1973) Zbl0279.58003MR0339002
  6. A. Gray, Geodesic balls in Riemannian product manifolds, in: M. Cahen and M. Flato (eds.), Differential Geometry and Relativity, Reidel, Dordrecht, 1976. (1976) Zbl0345.53007MR0438252
  7. A. Gray, L. Vanhecke, Riemannian geometry as determined by the volumes of small geodesic balls, Acta math. 142 (1979), 157-198. (1979) Zbl0428.53017MR0521460
  8. P. Günther, Einige Sätze über das Volumenelement eines Riemannschen Raumes, Publ. Math. Debrecen 7 (1960), 78-93. (1960) MR0141058
  9. O. Kowalski, Additive volume invariants of Riemannian manifolds, Acta math. 145 (1980), 205-225. (1980) Zbl0454.53031MR0590290
  10. O. Kowalski, The volume conjecture and four-dimensional hypersurfaces, Comment. Math. Univers. Carol. 23 (1982), 81-87. (1982) Zbl0489.53050MR0653352
  11. O. Kowalski, L. Vanhecke, Ball-homogeneous and disk-homogeneous Riemannian manifolds, Math. Z. 180 (1982), 429-444. (1982) Zbl0476.53023MR0666999
  12. O. Kowalski, L. Vanhecke, On disk-homogeneous symmetric spaces, Ann. Glob. Analysis and Geom. 1 (1983), 91-104. (1983) Zbl0533.53047MR0739899
  13. O. Kowalski, L. Vanhecke, The volume of geodesic disks in a Riemannian manifold, Czech. Math. J. 35 (1985), 66-77. (1985) Zbl0586.53006MR0779337
  14. O. Kowalski, L. Vanhecke, Two-point functions on Riemannian manifolds, Ann. Glob. Analysis and Geom. 3 (1985), 95-119. (1985) Zbl0571.53031MR0812315
  15. A. Lichnerowicz, A. G. Walker, Sur les espaces riemanniens harmoniques de type hyperbolique normal, C. R. Acad. Sc. Paris 221 (1945), 394-396. (1945) Zbl0060.38507MR0015269
  16. V. Miquel, The volumes of small geodesic balls for a metric connection, Compositio Math. 46 (1982), 121-132. (1982) Zbl0489.53043MR0660156
  17. V. Miquel, Volumes of certain small geodesic balls and almost Hermitean geometry, Geometriae Dedicata 15 (1984), 261 -267. (1984) MR0739929
  18. H. S. Ruse A. G. Walker, and T. J. Willmore, Harmonic Spaces, Edizioni Cremonese, Roma, 1961. (1961) MR0142062
  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. (1985) Zbl0571.53012MR0807133

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.