Geodesic
On the Lichnerovicz Laplacian
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 2, Tome 169 (2019), pp. 67-74

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

In this paper, we study the geometry of the kernel of the Lichnerovicz Laplacian in the case of complete and, in particular, compact Riemannian manifolds, and also propose a lower estimate of its eigenvalues on a compact Riemannian manifold with the curvature operator bounded from below and an upper estimate of its eigenvalues on a compact Riemannian manifold with the Ricci curvature bounded from below. We define the Lichnerovicz Laplacian on the space of smooth sections of the bundle of covariant tensors as is required by its original definition; this distinguishes our results from results obtained earlier.
Keywords: Riemannian manifold, covariant tensor, kernel of the Laplacian, eigenvalue of the Laplacian.
Mots-clés : Lichnerovicz Laplacian 
@article{INTO_2019_169_a8,
     author = {S. E. Stepanov and I. I. Tsyganok},
     title = {On the {Lichnerovicz} {Laplacian}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {67--74},
     publisher = {mathdoc},
     volume = {169},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_169_a8/}
}
TY  - JOUR
AU  - S. E. Stepanov
AU  - I. I. Tsyganok
TI  - On the Lichnerovicz Laplacian
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 67
EP  - 74
VL  - 169
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_169_a8/
LA  - ru
ID  - INTO_2019_169_a8
ER  - 
%0 Journal Article
%A S. E. Stepanov
%A I. I. Tsyganok
%T On the Lichnerovicz Laplacian
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 67-74
%V 169
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_169_a8/
%G ru
%F INTO_2019_169_a8
S. E. Stepanov; I. I. Tsyganok. On the Lichnerovicz Laplacian. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 2, Tome 169 (2019), pp. 67-74. http://geodesic.mathdoc.fr/item/INTO_2019_169_a8/