Abstract |
| Geometric monotone properties of the first non-zero eigenvalue of Laplacian form operator under the action of the Ricci flow in a compact n-manifold are studied. We introduce certain energy functional which proves to be monotonically nondecreasing, as an application, we show that all steady breathers are gradient steady solitons, which are Ricci flat metric. The results are also extended to the case of normalized Ricci flow, where we establish nonexistence of expanding breathers other than gradient solitons. |
Keywords and phrases
eigenvalues, Laplace-Beltrami operator, Ricci breathers, Ricci soliton, entropy formulae.
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FRDI Journals 
