Geodesic
g -Natural metrics on tangent bundles and Jacobi operators
Acta mathematica Universitatis Comenianae, Tome 80 (2011) no. 2 
S. Degla; L. Todjihounde. g -Natural metrics on tangent bundles and Jacobi operators. Acta mathematica Universitatis Comenianae, Tome 80 (2011) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2011_80_2_a10/
@article{AMUC_2011_80_2_a10,
     author = {S. Degla and L. Todjihounde},
     title = {g {-Natural} metrics on tangent bundles and {Jacobi} operators},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2011},
     volume = {80},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2011_80_2_a10/}
}
TY  - JOUR
AU  - S. Degla
AU  - L. Todjihounde
TI  - g -Natural metrics on tangent bundles and Jacobi operators
JO  - Acta mathematica Universitatis Comenianae
PY  - 2011
VL  - 80
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AMUC_2011_80_2_a10/
ID  - AMUC_2011_80_2_a10
ER  - 
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%A L. Todjihounde
%T g -Natural metrics on tangent bundles and Jacobi operators
%J Acta mathematica Universitatis Comenianae
%D 2011
%V 80
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_2011_80_2_a10/
%F AMUC_2011_80_2_a10

Voir la notice de l'article provenant de la source Comenius University

Let ( M, g ) be a Riemannian manifold and G a nondegenerate g -natural metric on its tangent bundle TM . In this paper we establish a relation between the Jacobi operators of ( M, g ) and that of ( TM, G ). In the case of a Riemannian surface ( M, g ), we compute explicitly the spectrum of some Jacobi operators of ( TM, G ) and give necessary and sufficient conditions for ( TM, G ) to be an Osserman manifold.