Geodesic
Some conformal and projective scalar invariants of Riemannian manifolds
Matematičeskie zametki, Tome 80 (2006) no. 6, pp. 902-907.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that, on any closed oriented Riemannian $n$-manifold, the vector spaces of conformal Killing, Killing, and closed conformal Killing $r$-forms, where $1\le r\le n-1$, have finite dimensions $t_r$, $k_r$, and $p_r$, respectively. The numbers $t_r$ are conformal scalar invariants of the manifold, and the numbers $k_r$ and $p_r$ are projective scalar invariants; they are dual in the sense that $t_r=t_{n-r}$ and $k_r=p_{n-r}$. Moreover, an explicit expression for a conformal Killing $r$-form on a conformally flat Riemannian $n$-manifold is given. 
@article{MZM_2006_80_6_a7,
     author = {S. E. Stepanov},
     title = {Some conformal and projective scalar invariants of {Riemannian} manifolds},
     journal = {Matemati\v{c}eskie zametki},
     pages = {902--907},
     publisher = {mathdoc},
     volume = {80},
     number = {6},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_6_a7/}
}
TY  - JOUR
AU  - S. E. Stepanov
TI  - Some conformal and projective scalar invariants of Riemannian manifolds
JO  - Matematičeskie zametki
PY  - 2006
SP  - 902
EP  - 907
VL  - 80
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_80_6_a7/
LA  - ru
ID  - MZM_2006_80_6_a7
ER  - 
%0 Journal Article
%A S. E. Stepanov
%T Some conformal and projective scalar invariants of Riemannian manifolds
%J Matematičeskie zametki
%D 2006
%P 902-907
%V 80
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2006_80_6_a7/
%G ru
%F MZM_2006_80_6_a7
S. E. Stepanov. Some conformal and projective scalar invariants of Riemannian manifolds. Matematičeskie zametki, Tome 80 (2006) no. 6, pp. 902-907. http://geodesic.mathdoc.fr/item/MZM_2006_80_6_a7/

[1] A. Besse, Mnogoobraziya Einshteina, t. I, Mir, M., 1990 | MR | Zbl

[2] S. E. Stepanov, “Teoremy ischeznoveniya v affinnoi, rimanovoi i lorentsevoi geometriyakh”, Fundament. i prikl. matem., 11:1 (2005), 35–84 | MR | Zbl

[3] S. E. Stepanov, “O tenzore Killinga–Yano”, TMF, 134:3 (2003), 382–387 | MR

[4] R. Narasimkhan, Analiz na deistvitelnykh i kompleksnykh mnogoobraziyakh, Mir, M., 1971 | MR | Zbl

[5] S. E. Stepanov, “On conformal Killing 2-form of the electromagnetic field”, J. Geom. Phys., 33:3–4 (2000), 191–209 | DOI | MR | Zbl

[6] S. E. Stepanov, “Novyi silnyi laplasian na differentsialnykh formakh”, Matem. zametki, 76:3 (2004), 452–458 | MR | Zbl

[7] T. Branson, “Stein–Weiss operators and ellipticity”, J. Funct. Anal., 151:2 (1997), 334–383 | DOI | MR | Zbl

[8] R. Pale, Seminar po teoreme Ati–Zingera ob indekse, Mir, M., 1970 | MR

[9] M. Kora, “On conformal Killing forms and the proper space of $\Delta$ for $p$-forms”, Math. J. Okayama Univ., 22 (1980), 195–204 | MR | Zbl

[10] T. Kashiwada, “On conformal Killing tensor”, Nat. Sci. Rep. Ochanomizu Univ., 19 (1968), 67–74 | MR | Zbl