Huygens' principle on Petrov type N space-times

V. Wünsch

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

  • Volume: 61, Issue: 1, page 87-102
  • ISSN: 0246-0211

How to cite

top

Wünsch, V.. "Huygens' principle on Petrov type N space-times." Annales de l'I.H.P. Physique théorique 61.1 (1994): 87-102. <http://eudml.org/doc/76649>.

@article{Wünsch1994,
author = {Wünsch, V.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Huygens' principle; scalar wave equation; Maxwell's equations; Weyl's equation; plane gravitational wave; Petrov type},
language = {eng},
number = {1},
pages = {87-102},
publisher = {Gauthier-Villars},
title = {Huygens' principle on Petrov type N space-times},
url = {http://eudml.org/doc/76649},
volume = {61},
year = {1994},
}

TY - JOUR
AU - Wünsch, V.
TI - Huygens' principle on Petrov type N space-times
JO - Annales de l'I.H.P. Physique théorique
PY - 1994
PB - Gauthier-Villars
VL - 61
IS - 1
SP - 87
EP - 102
LA - eng
KW - Huygens' principle; scalar wave equation; Maxwell's equations; Weyl's equation; plane gravitational wave; Petrov type
UR - http://eudml.org/doc/76649
ER -

References

top
  1. [A] M. Alvarez, Zum Huygensschen Prinzip bei einigen Klassen spinorieller Feldgleichungen in gekrümmten Raum-Zeit-Mannigfaltrigkeiten, Dissertation A, Pädgogische Hochschule. 
  2. [AW] M. Alvarez and V. Wünsch, Zur Gültigkeit des Huygensschen Prinzips bei der Weyl-Gleichung und den homogenen Maxwellschen Gleichunge für Metriken vom Petrow-Typ N, Wiss. Zeitschr. d. Päd. Hochschule Erfurt/Mühlhausen, Math.-naturwissensch. Reihe 27, 1991, H. 2, pp. 77-91. 
  3. [B] Y. Bruhat, Sur la théorie des propagateurs, Ann. Mat. Pura Appl., Vol. 64, 1964, pp. 191-228. Zbl0173.36501MR169659
  4. [CM] J. Carminati and R.G. Mclenaghan, An Explicit Determination of the Spacetimes on Which the Conformally Invariant Scalar Wave Equation Satisfies Huygens' Principle, Ann. Inst. Henri Poincaré, Phys. théor., Vol. 44, 1986, pp. 115-153; Part. II, Vol. 47, 1987, pp. 337-354; Part. III, Vol. 48, 1988, pp. 77-96; Vol. 54, 1991, p. 9. Zbl0595.35067
  5. [DC] L. Defrise-Carter, Conformal Groups and Conformally Equivalent Isometry Groups, Comm. Math. Phys., Vol. 40, 1975, pp. 273-282. Zbl0322.53008MR423241
  6. [F] F.G. Friedlander, The Wave Equation on a Curved Space-time, Cambridge University Press; Cambridge, London, New York, Melbourne, 1975. Zbl0316.53021MR460898
  7. [GeW1] R. Gerlach and V. Wünsch, Über konforminvariante Tensoren ungerader Stufe in gekrümmten Raum-Zeiten, Wiss. Zeitschr. d. Päd. Hochschule Erfurt-Mühlhausen, Math.-naturwissensch. Reihe 26, 1990, H. 1, pp. 20-32. Zbl0719.53055MR1102666
  8. [GeW2] R. Gerlach and V. Wünsch, Über konforminvariante Tensoren der Stufe sechs in gekrümmten Raum-Zeiten, Wiss. Zeitschr. d. Päd. Hochschule Erfurt-Mühlhausen, Math.-naturwissensch. Reihe 27, 1991, H. 2, pp. 117-143. 
  9. [G1] P. Günther, Spinorkalkül und Normakoordinaten, ZAMM, Vol. 55, 1975, pp. 205- 210 Zbl0324.53012MR452436
  10. [G2] P. Günther, Einige Sätze über Huygenssche Differentialgleichungen. Wiss. Zs. Karl-Marx-Univ. Leipzig, Vol. 14, 1965, pp. 497-507. Zbl0173.12203MR198012
  11. [G3] P. Günther, Ein Beispiel einer nichttrivialen Huygensschen Differentialgleichung mit vier unabhängigen Veränderlichen. Archive Rat. Mech. and Analysis, Vol. 18, 1965, pp. 103-106. Zbl0125.05404MR174865
  12. [G4] P. Günther, Huygens' Principle and Hyperbolic Equations, Boston, Academic Press, 1988. Zbl0655.35003MR946226
  13. [GW1] P. Günther and V. Wünsch, Maxwellsche Gleichungen und Huygenssches Prinzip I, Math. Nachr., Vol. 63, 1974, pp. 97-121. Zbl0288.35042MR363377
  14. [GW2] P. Günther and V. Wünsch, Contributions to a theory of polynomial conformal tensors, Math. Nachr., Vol. 126, 1986, pp. 83-100. Zbl0636.53025MR846571
  15. [GW3] P. Günther and V. Wünsch, On Some Polynomial Conformal Tensors, Math. Nachr, Vol. 124, 1985, pp. 217-238. Zbl0592.53012MR827899
  16. [Ha] J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Yale University Press, New Haven, 1923. Zbl49.0725.04JFM49.0725.04
  17. [He] S. Helgason, Huygens' Principle for Wave Equations on Symmetric Spaces, J. Funkt. Anal., Vol. 107, 1992, pp. 279-288. Zbl0757.58036MR1172025
  18. [I] R. Illge, Zur Gültigkeit des Huygensschen Prinzips bei hyperbolischen Differentialgleichungssystemen in statischen Raum-Zeiten, Zs. für Anal. und Anwendungen, Vol. 6, 1987, (5) pp. 385-407. Zbl0636.35073MR923526
  19. [L] A. Lichnerowicz, Champs spinoriels et propagateurs en relativité générale, Bull. Soc. math. Fr., Vol. 92, 1964, pp. 11-100. Zbl0138.44301MR169667
  20. [McL1] R.G. Mclenaghan, An Explicit Determination of the Empty Space-times on which the Wave Equation Satisfies Huygens' Principle, Proc. Cambridge Phil. Soc., Vol. 65, 1969, pp. 139-155. Zbl0182.13403MR234700
  21. [McL2] R.G. Mclenaghan, On the Validity of Huygens' Principle for Second Order Partial Differential Equations With Four Independent Variables. Part. I. Derivation of Necessary Conditions, Ann. Inst. H. Poincaré, Vol. A 20, 1974, pp. 153-188. Zbl0287.35058MR361452
  22. [McL3] R.G. McLenaghan, Huygens' principle, Ann. Inst. H. Poincaré, Vol. A 37, 1982, pp. 211-236. Zbl0528.35057MR694586
  23. [McL, L] R.G. Mclenaghan and J. Leroy, Complex Recurrent Space-Times. Proc. Roy. Soc. London, Vol. A 327, 1972, pp. 229-249. Zbl0243.53030MR309517
  24. [McL, W] R.G. Mclenaghan and 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. Henri Poincaré, Vol. A 53, 1990, p. 217. Zbl0709.53053
  25. [Ø] B. Ørsted, The Conformal Invariance of Huygens' Principle, Diff. Geom., Vol. 16, 1981, pp. 1-9. Zbl0447.35059MR633620
  26. [PR] R. Penrose and W. Rindler, Spinors and Space-time, Vol. 1, 1984, Vol. 2, 1986, Cambridge Univ. Press. MR776784
  27. [RW] B. Rinke and V. Wünsch, Zum Huygensschen Prinzip bei der skalaren Wellengleichung, Beiträge zur Analysis, Vol. 18, 1981, pp. 43-75. Zbl0501.53010MR650138
  28. [S1] R. Schimming, Zur Gültigkeit des Huygensschen Prinzips bei einer speziellen Metrik, ZAMM, Vol.51, 1971, pp. 201-208. Zbl0221.35011MR290313
  29. [S2] R. Schimming, Riemannsche Räume mit ebenfrontiger und ebener Symmetric, Math. Nachr, Vol. 59, 1974, pp. 129-162. Zbl0274.53049MR339774
  30. [W1] V. Wünsch, Über selbstadjungierte huygenssche Differentialgleichungen, Math. Nachr., Vol. 47, 1970, pp. 131-154. Zbl0211.40803MR298221
  31. [W2] V. Wünsch, Maxwellsche Gleichungen und Huygenssches Prinzip II, Math. Nachr., Vol. 73, 1976, pp. 19-36. Zbl0288.35043MR426807
  32. [W3] V. Wünsch, Über eine Klasse konforminvarianter Tensoren, Math. Nachr., Vol. 73, 1976, pp. 37-58. Zbl0287.53014MR433342
  33. [W4] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichungen I, II, Beiträge zur Analysis, Vol. 12, 1978, pp. 47-76; Vol. 13, 1979, pp. 147-177. Zbl0467.35067MR507097
  34. [W5] V. Wünsch, Konforminvariante Variationsprobleme und Huygenssches Prinzip, Math. Nachr., Vol.120, 1985, pp. 175-193. MR808340
  35. [W6] V. Wünsch, C-Räume und Huygenssches Prinzip, Wiss. Zeitscher. d. Päd. Hochschule Erfurt-Mühlhausen, Math.-naturwissensch, Reihe 23, 1987, H. 1, pp. 103-111. Zbl0627.53057MR910678
  36. [W7] V. Wünsch, Huygens' Principle on Petrov Type D Space-Times, Ann. d. Physik, 7. Folge, Bd. 46, H. 8, 1989, pp. 593-597. Zbl0697.53027MR1051239
  37. [W8] V. Wünsch, Moments and Huygens' Principle for Conformally Invariant Field Equations in Curved Space Times, Ann. Inst. Henri Poincaré, Vol. A60, 4, 1994. Zbl1010.58503MR1288587

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.