Geodesic
Dimensional Reduction of Conformal Tensors and Einstein–Weyl Spaces
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Conformal Weyl and Cotton tensors are dimensionally reduced by a Kaluza–Klein procedure. Explicit formulas are given for reducing from four and three dimensions to three and two dimensions, respectively. When the higher dimensional conformal tensor vanishes because the space is conformallly flat, the lower-dimensional Kaluza–Klein functions satisfy equations that coincide with the Einstein–Weyl equations in three dimensions and kink equations in two dimensions.
Keywords: conformal tensors; dimensional reductions; Kaluza–Klein. 
@article{SIGMA_2007_3_a90,
     author = {R. W. Jackiw},
     title = {Dimensional {Reduction} of {Conformal} {Tensors} and {Einstein{\textendash}Weyl} {Spaces}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2007},
     volume = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a90/}
}
TY  - JOUR
AU  - R. W. Jackiw
TI  - Dimensional Reduction of Conformal Tensors and Einstein–Weyl Spaces
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2007
VL  - 3
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a90/
LA  - en
ID  - SIGMA_2007_3_a90
ER  - 
%0 Journal Article
%A R. W. Jackiw
%T Dimensional Reduction of Conformal Tensors and Einstein–Weyl Spaces
%J Symmetry, integrability and geometry: methods and applications
%D 2007
%V 3
%U http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a90/
%G en
%F SIGMA_2007_3_a90
R. W. Jackiw. Dimensional Reduction of Conformal Tensors and Einstein–Weyl Spaces. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a90/

[1] Bergmann P. G., Introduction to the theory of relativity, Prentice Hall, New York, 1942 | MR

[2] Grumiller D., Jackiw R., “Kaluza–Klein reduction of conformally flat spaces”, Intern. J. Modern Phys. D, 15 (2006), 2075–2094 ; math-ph/0609025 | DOI | MR

[3] Guralnik G., Iorio A., Jackiw R., Pi S. Y., “Dimensionally reduced gravitational Chern–Simons term and its kink”, Ann. Physics, 308 (2003), 222–236 ; hep-th/0305117 | DOI | MR | Zbl

[4] Grumiller D., Kummer W., “The classical solutions of the dimensionally reduced gravitational Chern–Simons theory”, Ann. Physics, 308 (2003), 211–221 ; hep-th/0306036 | DOI | MR | Zbl

[5] Cacciatori S., Calderelli M., Klemm D., Mansi D., “More on BPS solutions of $N=2$, $D=4$ gauged supergravity”, JHEP, 2004:7 (2004), 061, 31 pp., ages ; ; Bergamin L., Grumiller D., Iorio A., Nuñez C., “Chemistry of Chern–Simons supergravity: reduction to a BPS kink, oxidation to $M$-theory and thermodynamical aspects”, JHEP, 2004:11 (2004), 021, 40 pp., ages ; ; Sahoo B., Sen A., “BTZ black hole with Chern–Simons and higher derivative terms”, JHEP, 2006:7 (2006), 008, 11 pp., ages ; ; Sahoo B., Sen A., “$\alpha'$-correction to external dyonic black holes in heterofic string theory”, JHEP, 2007:1 (2007), 010, 18 pp., ages ; hep-th/0406238hep-th/0409273hep-th/0601228hep-th/0608182 | DOI | MR | DOI | MR | DOI | MR | DOI | MR

[6] Eastwood M., Private communication

[7] Jones P., Tod K., “Minitwistor spaces and Einstein–Weyl spaces”, Classical Quantum Gravity, 2 (1985), 565–577 ; Tod K., “Compact 3-dimensional Einstein–Weyl structures”, J. Lond. Math. Soc. (2), 42 (1992), 341–351 ; Eastwood M., Tod K., “Local constraints on Einstein–Weyl geometries”, J. Reine Angew. Math., 491 (1997), 183–198 | DOI | MR | Zbl | DOI | MR | MR | Zbl