Contributions to polynomial conformal tensors
Annales de l'I.H.P. Physique théorique (1999)
- Volume: 70, Issue: 3, page 313-340
- ISSN: 0246-0211
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topGerlach, R., and Wünsch, V.. "Contributions to polynomial conformal tensors." Annales de l'I.H.P. Physique théorique 70.3 (1999): 313-340. <http://eudml.org/doc/76818>.
@article{Gerlach1999,
author = {Gerlach, R., Wünsch, V.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {conformally equivalent; conformally invariant tensor; pseudo-Riemannian manifold; Huygens' principle; Einstein space-time},
language = {eng},
number = {3},
pages = {313-340},
publisher = {Gauthier-Villars},
title = {Contributions to polynomial conformal tensors},
url = {http://eudml.org/doc/76818},
volume = {70},
year = {1999},
}
TY - JOUR
AU - Gerlach, R.
AU - Wünsch, V.
TI - Contributions to polynomial conformal tensors
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 70
IS - 3
SP - 313
EP - 340
LA - eng
KW - conformally equivalent; conformally invariant tensor; pseudo-Riemannian manifold; Huygens' principle; Einstein space-time
UR - http://eudml.org/doc/76818
ER -
References
top- [AW] M. Alvarez and V. Wünsch, Zur Gültigkeit des Huygensschen Prinzips bei der Weyl-Gleichung und den homogenen Maxewellschen Gleichungen für Metriken vom Petrow-Typ N, Wiss. Zeitschr. der Päd. Hochschule Erfurt/Mühlhausen, Math.-Naturwissensch. Reihe, 27, 1991, H.2., pp. 77-91.
- [AMLW] W.G. Anderson, R.G. Mclenaghan and T.F. Walton, An explicit determination of the non-self-adjoint wave equations that satisfy Huygens' principle on Petrov type III background space-times, Z.f. Anal. u. ihre Anw., 16, 1997, 1, pp. 37-58. Zbl0885.35062MR1453390
- [Ba] J.R. Baston, Verma Modules and Differential Conformal Invariants, J. Differential Geometrie, 32, 1990, pp. 851-898. Zbl0732.53011MR1078164
- [BE] J.R. Baston, and M.G. Eastwood, Invariant operators, Twistors in Mathematics and Physics, LMS Lecture Notes156, (eds. BAILY and BASTON) Cambridge University Press, 1990. MR1089914
- [BØ] T. Branson and B. Ørsted B., Conformal indices of Riemannian manifolds, Composito Mathematica, 60, 1986, pp. 261-293. Zbl0608.58039MR869104
- [Bra] T. Branson, Differential Operators Canonically Associated to a Conformal Structure, Mathematica Scandinavica, 57, 1985, pp. 293-345. Zbl0596.53009MR832360
- [Bri] H.W. Brinkman, Riemann spaces conformal to Einstein spaces, Math. Ann., 91, 1924, pp. 269-287. MR1512193JFM50.0504.01
- [CMcL] J. Carminati and R.G. Mclenaghan, An explicit determination of the space-times 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
- [dP] J.C. Du Plessis, Polynomial conformal tensors, Proc. Camb. Phil. Soc., 68, 1970, pp. 329-344. Zbl0203.54603MR259802
- [E] M.G. Eastwood, The Fefferman Graham conformal invariant, Twistor Newsletter, 20, 1985, p. 46.
- [FG] C. Fefferman and C.R. Graham, Conformal invariants, Élie Cartan et les Mathématiques d'Aujourd'hui, Astérisque, 1985, pp. 95-116. Zbl0602.53007MR837196
- [Ge] R. Gerlach, Beiträge zur konformen Geometrie in drei- und vierdimensionalen pseudo-Riemannschen Räumen, DIssertation A, Pädagogische Hochschule Erfurt, 1996.
- [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, 20-32. Zbl0719.53055MR1102666
- [GeW2] Gerlach R. 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, 117-143.
- [Gü] P. Günther, Huygens' Principle and Hyperbolic Equations, Academic Press, Boston, 1988. Zbl0655.35003MR946226
- [GüW1] P. Günther and V. Wünsch, Contributions to a theory of polynomial conformal tensors, Math. Nachr., 126, 1986, pp. 83-100. Zbl0636.53025MR846571
- [GüW2] P. Günther and V. Wünsch, On some polynomial conformal tensors, Math. Nach., 124, 1985, pp. 217-238. Zbl0592.53012MR827899
- [Il] 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
- [KNT] C.N. Kozamek, E.T. Newman and K.P. Tod, Conformal Einstein-spaces, Gen. Rel. and Grav., 17, 4, 1985, pp. 343-352. Zbl0564.53011MR788800
- [Lo] D. Lovelock, Dimensionally dependent identities, Proc. Camb. Phil. Soc., 68, 1970, pp. 345-350. Zbl0197.48301MR260389
- [McL] R.G. Mclenaghan, An explicit determination of the empty space-times on which the wave equation satisfies Huygens' principle, Proc. Cambridge Philos. Soc., 65, 1969, pp. 139-155. Zbl0182.13403MR234700
- [McLS] R.G. Mclenaghan and F.D. Sasse, Nonexistence of Petrov-type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle, Ann. Inst. Henri Poincaré, Phys. Théor., 65, 1996, pp. 253-271. Zbl0869.53061MR1420704
- [Ø] B. Ørsted, The Conformal Invariance of Huygens' Principle, Diff. Geom., 16, 1981, pp. 1-9. Zbl0447.35059MR633620
- [PR] R. Penrose and W. Rindler, Spinors and Space-Time I, II, Cambridge University Press, 1984, 1986.
- [RW] B. Rinke and V. Wünsch, Zum Huygensschen Prinzip bei der skalaren Wellengleichung, Beiträge zur Analysis, 18, 1981, pp. 43-75. Zbl0501.53010MR650138
- [Schi] R. Schimming, Konforminvarianten vom Gewicht -1 eines Zusammenhanges oder Eichfeldes, Zeitschrift für Analysis und ihre Anwendungen, 3 (5), 1984, pp. 401- 412. Zbl0563.53024MR777675
- [Scho] J.A. Schouten and Ricci-Calculus, Springer-Verlag, Berlin, 1954. MR516659
- [Sz] P. Szekeres, Conformal tensors, Proc. Roy. Soc. A., 304, 1968, pp. 113-122. Zbl0159.23903
- [Tho] T.Y. Thomas, Conformal tensors, Proc. of the Nat. Acad. of Sci, Washington, 12 (152), 1926, 18 (103u. 189), 1932. Zbl0003.41307
- [Thi] R. Thielken, Herleitung einiger neuer Identitäten für den Konformkrümmungs tensor mit Hilfe des Spinorkalküls, Diplomarbeit, Universität Leipzig, Pädagogische Hochschule Erfurt, 1989.
- [Wü1] V. Wünsch, Über eine Klasse konforminvarianter Tensoren, Math. Nachr., 73, 1976, pp. 37-58. Zbl0287.53014MR433342
- [Wü2] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichungen I, II, Beitr. zu Analysis, 12, 1978, pp. 47-76; 13, 1979, pp. 147-177. Zbl0448.58022MR507097
- [Wü3] V. Wünsch, Huygens' principle on Petrov type D Space-Times, Ann. d. Physik, 7.Folge, 46 (8), 1989, pp. 593-597. Zbl0697.53027MR1051239
- [Wü4] V. Wünsch, Conformal C- and Einstein Spaces, Math. Nach., 146, 1990, pp. 237- 245. Zbl0711.53019MR1069065
- [Wü5] V. Wünsch, Moments and Huygens' principle for conformally invariant field equation in curved space-times, Ann. Inst. Henri Poincaré, Physique théorique, 60, (4), 1994, pp. 433-455. Zbl1010.58503MR1288587
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