Geodesic
On the Global Geometry of Harmonic Symmetric Bilinear Differential Forms
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 328-331 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A harmonic symmetric $p$-form $\varphi$ is defined as an element of the kernel of a self-adjoint differential operator $\square$. By using the properties of this operator, the dimension of the $\mathbb R$-modulus of harmonic symmetric $p$-forms is shown to be finite on a compact Riemannian manifold. A nonexistence theorem is proved for harmonic symmetric $2$-forms tangent to the boundary of a compact Riemannian manifold. 
@article{TM_2002_236_a32,
     author = {M. V. Smolnikova},
     title = {On the {Global} {Geometry} of {Harmonic} {Symmetric} {Bilinear} {Differential} {Forms}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {328--331},
     year = {2002},
     volume = {236},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_236_a32/}
}
TY  - JOUR
AU  - M. V. Smolnikova
TI  - On the Global Geometry of Harmonic Symmetric Bilinear Differential Forms
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2002
SP  - 328
EP  - 331
VL  - 236
UR  - http://geodesic.mathdoc.fr/item/TM_2002_236_a32/
LA  - ru
ID  - TM_2002_236_a32
ER  - 
%0 Journal Article
%A M. V. Smolnikova
%T On the Global Geometry of Harmonic Symmetric Bilinear Differential Forms
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2002
%P 328-331
%V 236
%U http://geodesic.mathdoc.fr/item/TM_2002_236_a32/
%G ru
%F TM_2002_236_a32
M. V. Smolnikova. On the Global Geometry of Harmonic Symmetric Bilinear Differential Forms. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 328-331. http://geodesic.mathdoc.fr/item/TM_2002_236_a32/

[1] Sumitomo T., Tandai K., “Killing tensor fields on the standard sphere and spectra of $SO(n+1)/SO(n-1)\times SO(2)$ and $O(n+1)/O(n-1)\times O(2)$”, Osaka J. Math., 20 (1983), 51–78 | MR | Zbl

[2] Yano K., Bochner S., Curvature and Betti numbers, Princeton Univ. Press, Princeton, NJ, 1953 | MR | Zbl

[3] Eisenhart L. P., Riemannian geometry, Princeton Univ. Press, Princeton, 1926 | MR | Zbl

[4] Palais R. S., Seminar on the Atiah–Singer index theorem, Princeton Univ. Press, Princeton, NJ, 1965 | MR | Zbl

[5] de Rham G., Varietes differentiables. Formes, courants, formes harmoniques, Hermann, Paris, 1955 | Zbl

[6] Besse A., Mnogoobraziya Einshteina, Springer-Verl., Berlin, 1987 | MR

[7] Bourguignon J. P., Formules de Weizenböck en dimension 4, Séminare A. Besse sur la géométrie en dimension 4, Cedic, Fernan Nathan, Paris, 1981 | MR

[8] Stepanov S. E., Rodionov V. V., “Dopolnenie k odnoi rabote Zh.-P. Burginona”, Differentsialnaya geometriya mnogoobrazii figur, Univ. sb. nauch. rabot. No 28, Kaliningrad, 1997, 68–72 | Zbl