Abstract
In this paper, we introduce the Generalized Cheeger-Gromoll metric on the tangent bundle TM, as a natural metric on TM. We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the Generalized Cheeger-Gromoll metric. We also construct some examples of harmonic vector fields.
Highlights
Horizontal lift, vertical lift, generalized Cheeger-Gromoll metric, harmonic maps
Consider a smooth map : (M m; g) ! (N n; h) between two Riemannian manifolds, the energy functional is de...ned by ZE( ) = e( )dvg (1)K or over any compact subset K M .e( ) = 2 traceg( h) = 2 tracegh(d ; d ) (2)is the energy density of .A map is called harmonic if it is a critical point of the energy functional
We introduce the Generalized Cheeger-Gromoll metric on the tangent bundle the map : (T M), as a natural metric on T M
Summary
Horizontal lift, vertical lift, generalized Cheeger-Gromoll metric, harmonic maps. [16], [21]Let (M; g) be a Riemannian manifold and (T M; ge) its tangent bundle equipped with the Generalized Cheeger-Gromoll metric.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
