Geodesic
Killing spinor-valued forms and the cone construction
Archivum mathematicum, Tome 52 (2016) no. 5, pp. 341-355 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

On a pseudo-Riemannian manifold $\mathbb{M}$ we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on $\mathbb{M}$ and parallel fields on the metric cone over $\mathbb{M}$ for spinor-valued forms.
On a pseudo-Riemannian manifold $\mathbb{M}$ we introduce a system of partial differential Killing type equations for spinor-valued differential forms, and study their basic properties. We discuss the relationship between solutions of Killing equations on $\mathbb{M}$ and parallel fields on the metric cone over $\mathbb{M}$ for spinor-valued forms.
DOI : 10.5817/AM2016-5-341
Classification : 35R01, 53C15, 53C27, 81R25
Keywords: pseudo-Riemannian spin manifolds; Killing type equations; cone construction; spinor-valued differential forms 
@article{10_5817_AM2016_5_341,
     author = {Somberg, Petr and Zima, Petr},
     title = {Killing spinor-valued forms and the cone construction},
     journal = {Archivum mathematicum},
     pages = {341--355},
     year = {2016},
     volume = {52},
     number = {5},
     doi = {10.5817/AM2016-5-341},
     mrnumber = {3610868},
     zbl = {06674909},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2016-5-341/}
}
TY  - JOUR
AU  - Somberg, Petr
AU  - Zima, Petr
TI  - Killing spinor-valued forms and the cone construction
JO  - Archivum mathematicum
PY  - 2016
SP  - 341
EP  - 355
VL  - 52
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2016-5-341/
DO  - 10.5817/AM2016-5-341
LA  - en
ID  - 10_5817_AM2016_5_341
ER  - 
%0 Journal Article
%A Somberg, Petr
%A Zima, Petr
%T Killing spinor-valued forms and the cone construction
%J Archivum mathematicum
%D 2016
%P 341-355
%V 52
%N 5
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2016-5-341/
%R 10.5817/AM2016-5-341
%G en
%F 10_5817_AM2016_5_341
Somberg, Petr; Zima, Petr. Killing spinor-valued forms and the cone construction. Archivum mathematicum, Tome 52 (2016) no. 5, pp. 341-355. doi: 10.5817/AM2016-5-341

[1] Bär, C.: Real Killing spinors and holonomy. Communications in Mathematical Physics 154 (1993), 509–521. | DOI | MR | Zbl

[2] Baum, H., Friedrich, T., Grunewald, R., Kath, I.: Twistors and Killing spinors on Riemannian manifolds. Teubner-Texte zur Mathematik [Teubner Texts in Mathematics], B. G. Teubner Verlagsgesellschaft, 1991. | MR | Zbl

[3] Berger, M.: Sur les groupes d’holonomie homogènes de variétés à connexion affine et des variétés riemanniennes. Bulletin de la Société Mathématique de France 83 (1955), 279–308. | MR | Zbl

[4] Bohle, C.: Killing spinors on Lorentzian manifolds. J. Geom. Phys. 45 (3–4) (2003), 285–308. | DOI | MR | Zbl

[5] Duff, M.J., Nilsson, B.E.W., Pope, C.N.: Kaluza-Klein supergravity. Physics Reports. A Review Section of Physics Letters, vol. 130 (1–2), 1986, pp. 1–142. | MR

[6] Duff, M.J., Pope, C.N.: Kaluza-Klein Supergravity and the Seven Sphere. Supersymmetry and Supergravity '82, Proceedings of the Trieste September 1982 School, World Scientific Press, 1983. | MR

[7] Friedrich, T.: Der erste Eigenwert des Dirac-Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung. Math. Nachr. 97 (1) (1980), 117–146. | DOI | MR | Zbl

[8] Friedrich, T.: On the conformal relation between twistors and Killing spinors. Proceedings of the Winter School “Geometry and Physics”, vol. 22 (2), Circolo Matematico di Palermo, 1990, pp. 59–75. | MR | Zbl

[9] Semmelmann, U.: Conformal Killing forms on Riemannian manifolds. Math. Z. 245 (2003), 503–527. | DOI | MR | Zbl

[10] Simons, J.: On the transitivity of holonomy systems. Ann. of Math. (2) 76 (2) (1962), 213–234. | DOI | MR | Zbl

[11] Slupinski, M.J.: A Hodge type decomposition for spinor valued forms. Ann. Sci. École Norm. Sup. (4) 29 (1996), 23–48. | DOI | MR | Zbl

[12] Somberg, P.: Killing tensor spinor forms and their application in Riemannian geometry. Hypercomplex analysis and applications, Trends in Mathematics, Birkhauser, 2011, pp. 233–247. | MR | Zbl

[13] Stein, E.M., Weiss, G.: Generalization of the Cauchy-Riemann equations and representations of the rotation group. Amer. J. Math. 90 (1968), 163–196. | DOI | MR | Zbl

[14] Tachibana, S.-I., Yu, W.N.: On a Riemannian space admitting more than one Sasakian structures. Tohoku Math. J. (2) 22 (4) (1970), 536–540. | DOI | MR | Zbl

[15] Walker, M., Penrose, R.: On quadratic first integrals of the geodesic equations for type $\lbrace 22\rbrace $ spacetimes. Comm. Math. Phys. 18 (1970), 265–274. | DOI | MR

[16] Yano, K.: Some remarks on tensor fields and curvature. Ann. of Math. (2) 55 (1952), 328–347. | DOI | MR | Zbl

[17] Zima, P.: (Conformal) Killing spinor valued forms on Riemannian manifolds. Thesis, Charles University in Prague (2014), Available online at: https://is.cuni.cz/webapps/zzp/detail/121806

Cité par Sources :