On the hyperbolic space, we give the spectrum of the Laplacian acting on trace free symmetric tensors fields of any rank.
Sur l’espace hyperbolique, nous donnons le spectre du Laplacien agissant sur les champs de tenseurs symétriques sans trace de tous rangs.
Accepted:
Published online:
Erwann Delay 1
@article{CRMATH_2021__359_5_625_0, author = {Erwann Delay}, title = {Spectre du {Laplacien} agissant sur les $r$-tenseurs sym\'etriques sur l{\textquoteright}espace hyperbolique}, journal = {Comptes Rendus. Math\'ematique}, pages = {625--630}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {5}, year = {2021}, doi = {10.5802/crmath.201}, language = {fr}, }
TY - JOUR AU - Erwann Delay TI - Spectre du Laplacien agissant sur les $r$-tenseurs symétriques sur l’espace hyperbolique JO - Comptes Rendus. Mathématique PY - 2021 SP - 625 EP - 630 VL - 359 IS - 5 PB - Académie des sciences, Paris DO - 10.5802/crmath.201 LA - fr ID - CRMATH_2021__359_5_625_0 ER -
Erwann Delay. Spectre du Laplacien agissant sur les $r$-tenseurs symétriques sur l’espace hyperbolique. Comptes Rendus. Mathématique, Volume 359 (2021) no. 5, pp. 625-630. doi : 10.5802/crmath.201. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.201/
[1] Non-trivial, static, geodesically complete, vacuum space-times with a negative cosmological constant. II : (n4), AdS/CFT correspondence : Einstein metrics and their conformal boundaries (IRMA Lectures in Mathematics and Theoretical Physics), Volume 8, European Mathematical Society, 2005, pp. 165-205 | Zbl
[2] Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., 10, Springer, 1987 | MR | Zbl
[3] Essential spectrum of the Lichnerowicz Laplacian on symmetric 2-tensors on asymptotically hyperbolic manifolds, J. Geom. Phys., Volume 43 (2002), pp. 33-44 | DOI | MR | Zbl
[4] TT-eigentensors for the Lichnerowicz laplacian on some asymptotically hyperbolic manifolds with warped products metrics, Manuscr. Math., Volume 123 (2007) no. 2, pp. 147-165 | DOI | MR | Zbl
[5] On static Poincaré–Einstein metrics, J. High Energy Phys., Volume 2015 (2015) no. 6, 51, 18 pages | Zbl
[6] Non-deformability of Einstein metrics, Osaka J. Math., Volume 15 (1978), pp. 419-433 | Zbl
[7] Fredholm operators and Einstein metrics on conformally compact manifolds, Memoirs of the American Mathematical Society, 864, American Mathematical Society, 2006 | Zbl
[8] Propagateurs et commutateurs en relativité générale, Publ. Math., Inst. Hautes Étud. Sci., Volume 10 (1961), pp. 5-56 | DOI | Numdam
[9] On a theorem of Chern, Trans. Am. Math. Soc., Volume 177 (1973), pp. 141-153 | DOI | MR | Zbl
[10] Higher-spin kinematics & no ghosts on quantum space-time in Yang–Mills matrix models, Adv. Theor. Math. Phys., Volume 25 (2021) no. 4 (to appear)
[11] Complete Riemannian manifolds and some vector fields, Trans. Am. Math. Soc., Volume 117 (1965), pp. 251-275 | DOI | MR | Zbl
Cited by Sources:
Comments - Policy