Moments and Huygens' principle for conformally invariant field equations in curved space-times

V. Wünsch

Annales de l'I.H.P. Physique théorique (1994)

  • Volume: 60, Issue: 4, page 433-455
  • ISSN: 0246-0211

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Wünsch, V.. "Moments and Huygens' principle for conformally invariant field equations in curved space-times." Annales de l'I.H.P. Physique théorique 60.4 (1994): 433-455. <http://eudml.org/doc/76641>.

@article{Wünsch1994,
author = {Wünsch, V.},
journal = {Annales de l'I.H.P. Physique théorique},
language = {eng},
number = {4},
pages = {433-455},
publisher = {Gauthier-Villars},
title = {Moments and Huygens' principle for conformally invariant field equations in curved space-times},
url = {http://eudml.org/doc/76641},
volume = {60},
year = {1994},
}

TY - JOUR
AU - Wünsch, V.
TI - Moments and Huygens' principle for conformally invariant field equations in curved space-times
JO - Annales de l'I.H.P. Physique théorique
PY - 1994
PB - Gauthier-Villars
VL - 60
IS - 4
SP - 433
EP - 455
LA - eng
UR - http://eudml.org/doc/76641
ER -

References

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  1. [A] M. Alvarez, Zum Huygensschen Prinzip bei einigen Klassen spinorieller Feldgleichungen in gekrümmten Raum-Zeit-Mannigfaltigkeitenn, Dissertation A, Pädgogische Hochschule Erfurt, 1991. 
  2. [AM] M. Alvarez, V. Wünsch, Zur Gültigkeit des Huygensschen Prinzips bei der Weyl-Gleichung und den homogenen Maxwellschen Gleichungen für Metriken vom Petrow-Typ N, Wiss. Zeitschr. d. Päd. Hochschule Erfurt/Mühlhausen, Math.- naturwissensch. Reihe27, 1991, H. 2, pp. 77-91. 
  3. [B] Y. Bruhat, Sur la théorie des propagateurs, Ann. Mat. Pura Appl., 64, 1964, pp. 191-228. Zbl0173.36501MR169659
  4. [CM] J. Carminati, R.G. Mc Lenaghan, An Explicit Determination of the Space-times on which the Conformally Invariant Scalar Wave Equation Satisfies Huygens' Principle, Ann. Inst. Henri Poinaré, Phys. théor. 44, 1986, pp. 115-153; Part. II, 47, 1987, pp. 337-354; Part. III, 48, 1988, pp. 77-96; 54, 1991, pp. 9-16. 
  5. [DC] L. Defrise-Carter, Conformal Groups and Conformally Equivalent Isometry Groups, Comm. Math. Phys.40, 1975, pp. 273-282. Zbl0322.53008MR423241
  6. [DP] J.-C. Du Plessis, Polynomial Conformal Tensors, Proc. Cambridge Phil. Soc., 68, 1970, pp. 329-344. Zbl0203.54603MR259802
  7. [F] F.G. Friedlander, The Wave Equation on a Curved Space-time, Cambridge University Press, Cambridge, London, New-York, Melbourne, 1975. Zbl0316.53021MR460898
  8. [GeW1] R. Gerlach, V. Wünsch, Über konforminvariante Tensoren ungerader Stufe in gekrümmten Raum-Zeiten, Wiss. Zeitschr. d. Päd. Hochschule Erfurt-Mühlhausen, Math.-naturwissensch., Reihe26, 1990, H. 1, pp. 20-32. Zbl0719.53055MR1102666
  9. [GeW2] R. Gerlach, V. Wünsch, Über konforminvariante Tensoren der Stufe sechs in gekrümmten Raum-Zeiten, Wiss. Zeitschr. d. Päd. Hochschule Erfurt-Mühlhausen, Math.-naturwissensch., Reihe27, 1991, H. 2, pp. 117-143. 
  10. [G1] P. Günther, Zur Gültigkeit des Huygensschen Prinzips bei partiellen Differentialgleichungen vom normalem hyperbolischen Typ., Ber. Verh. Sächs. Akad. d. Wiss. Leipzig, M.-nat. Klasse, 100, H. 2, 1952. Zbl0046.32201MR50136
  11. [G2] P. Günther, Einige Sätze über Huygenssche Differentialgleichungen, Wiss. Zs. Karl-Marx-Univ. Leipzig, 14, 1965, pp. 497-507. Zbl0173.12203MR198012
  12. [G3] P. Günther, Ein Beispiel einer nichttrivialen Huygensschen Differentialgleichung mit vier unabhängigen Veränderlichen, Arch. Rat. Mech. and Analysis, 18, 1965, pp. 103-106. Zbl0125.05404MR174865
  13. [G4] P. Günther, Huygen's Principle and Hyperbolic Equations, Boston, Academic Press, 1988. Zbl0655.35003MR946226
  14. [GW1] P. Günther, V. Wünsch, Maxwellsche Gleichungen und Huygenssches Prinzip, I. Math. Nachr., 63, 1974, pp. 97-121. Zbl0288.35042MR363377
  15. [GW2] P. Günther, V. Wünsch, Contributions to a Theory of Polynomial Conformal Tensors, Math. Nachr., 126, 1986, pp. 83-100. Zbl0636.53025MR846571
  16. [GW3] P. Günther, V. Wünsch, On some Polynomial Conformal Tensors, Math. Nachr., 124, 1985, pp. 217-238. Zbl0592.53012MR827899
  17. [Ha] J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Yale University Press, New Haven, 1923. Zbl49.0725.04JFM49.0725.04
  18. [He] S. Helgason, Huygens' Principle for Wave Equations on Symmetric Spaces, J. Funkt. Anal., 107, 1992, pp. 279-288. Zbl0757.58036MR1172025
  19. [I] R. Illge, Zur Gültigkeit des Huygensschen Prinzips bei hyperbolischen Differentialgleichungssystemen in statischen Raum-Zeiten, Zs. für Anal. und Anwendungen, 6, 1987, pp. 385-407. Zbl0636.35073MR923526
  20. [L] A. Lichnerowicz, Champs spinoriels et propagateurs en relativité générale, Bull. Soc. math. Fr., 92, 1964, pp. 11-100. Zbl0138.44301MR169667
  21. [McL1] R.G. Mc Lenaghan, An Explicit Determination of the Empty Space-Times on which the Wave Equation Satisfies Huygens' Principle. Proc. Cambridge Phil. Soc., 65, 1969, pp. 139-155. Zbl0182.13403MR234700
  22. [McL2] R.G. Mc Lenaghan, On the Validity of Huygen's Principle for Second Order Partial Differential Equations with four Independent Variables. Part. I. Derivation of Necessary Conditions, Ann. Inst. H. Poincaré, A 20, 1974, pp. 153-188. Zbl0287.35058MR361452
  23. [McL3] R.G. Mc Lenaghan, Huygens' Principle. Ann. Inst. H. Poincaré, A 37, 1982, pp. 211-236. Zbl0528.35057MR694586
  24. [McL, L] R.G. Mc Lenaghan, J. Leroy, Complex Recurrent Space-times. Proc. Roy. Soc. London, A 327, 1972, pp. 229-249. Zbl0243.53030MR309517
  25. [McL, W] R.G. Mc Lenaghan, G.C. Williams, An Explicit Determination of the Petrov Type D Space-Times on which Weyl's Neutrino Equation and Maxwell's Equations Satisfy Huygens' Principle. Ann. Inst. H. PoincaréA, 53, 1990, pp. 217-223. Zbl0709.53053MR1079778
  26. [O] B. Orsted, The Conformal Invariance of Huygens' Principle, Diff. Geom., 16, 1981, pp. 1-9. Zbl0447.35059MR633620
  27. [PR] R. Penrose, W. Rindler, Spinors and space-time, Vol. 1, 1984, Vol. 2, 1986, Cambridge Univ. Press. MR776784
  28. [RW] B. Rinke, V. Wünsch, Zum Huygensschen Prinzip bei der skalaren Wellengleichung. Beiträge zur Analysis, 18, 1981, pp. 43-75. Zbl0501.53010MR650138
  29. [Sch] E. Schmutzer, Relativistische Physik, B. G. Teubner-Verlag, Leipzig, 1968. Zbl0193.57301
  30. [S1] R. Schimming, Zur Gültigkeit des Huygensschen Prinzips bei einer speziellen Metrik. ZAMM, 51, 1971, pp. 201-208. Zbl0221.35011MR290313
  31. [S2] R. Schimming, Riemannsche Raüme mit ebenfrontiger und ebener Symmetrie, Math. Nachr., 59, 1974, pp. 129-162. Zbl0274.53049MR339774
  32. [S3] R. Schimming, Das Huygenssche Prinzip bei hyperbolischen Differentialgleichungen für allgemeine Felder. Beiträge zur Analysis11, 1978, pp. 45-90. Zbl0378.35042MR502738
  33. [W1] V. Wünsch, Über selbstadjungierte huygenssche Differentialgleichungen. Math. Nachr.47, 1970, pp. 131-154. Zbl0211.40803MR298221
  34. [W2] V. Wünsch, Maxwellsche Gleichungen und Huygenssches Prinzip II, Math. Nachr., 73, 1976, pp. 19-36. Zbl0288.35043MR426807
  35. [W3] V. Wünsch, Über eine Klasse konforminvarianter Tensoren, Math. Nachr., 73, 1976, pp. 37-58. Zbl0287.53014MR433342
  36. [W4] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei ennigen Klassen spinorieller Feldgleichung I, II, Beiträge zur Analysis, 12, 1978, pp. 47-76. 13, 1979, pp. 147-177. Zbl0467.35067MR507097
  37. [W5] V. Wünsch, Konforminvariante Variationsprobleme und Huygenssches Prinzip, Math. Nachr.120, 1985, pp. 175-193. MR808340
  38. [W6] V. Wünsch, C-Räume und Huygenssches Prinzip, Wiss. Zeitschr. d. Päd. Hochschule Erfurt-Mülhhausen, Math.-naturwissensch., Reihe, 23, 1987, H. 1, pp. 103-111. Zbl0627.53057MR910678
  39. [W7] V. Wünsch, Huygens' Principle on Petrov Typ D Space-Times, Ann. d. Physik, 7. Folge, Bd. 46, H. 8, 1989, pp. 593-597. Zbl0697.53027MR1051239
  40. [W8] V. Wünsch, Conformal C- and Einstein Spaces, Math. Nachr., 146, 1990, pp. 237- 245. Zbl0711.53019MR1069065

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