Some Bounds for the First Eigenvalue of a Generalized Laplace Operator

In this paper, by using extended Reilly formula and extended Bochner formula we find some lower bounds for the first eigenvalue of {\Delta _B}(u): = div(B\nabla u) - \left\langle {divB,\nabla u} \right\rangle , where B denotes a positive definite divergence free self-adjoint (۱,۱)-Codazzi tensor field on a compact Riemannian manifold M.

کلیدواژه ها:

Bochner technique ، Myers' theorem ، Cheeger-Gromoll splitting theorem ، Volume comparison theorem ، End of manifold