Geodesic
EIGENVALUES OF GEOMETRIC OPERATORS RELATED TO THE WITTEN LAPLACIAN UNDER THE RICCI FLOW
Glasgow mathematical journal, Tome 59 (2017) no. 3, pp. 743-751

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Let (M, g(t)) be a compact Riemannian manifold and the metric g(t) evolve by the Ricci flow. In the paper, we prove that the eigenvalues of geometric operator −Δφ + $\frac{R}{2}$ are non-decreasing under the Ricci flow for manifold M with some curvature conditions, where Δφ is the Witten Laplacian operator, φ ∈ C 2(M), and R is the scalar curvature with respect to the metric g(t). We also derive the evolution of eigenvalues under the normalized Ricci flow. As a consequence, we show that compact steady Ricci breather with these curvature conditions must be trivial. 
FANG, SHOUWEN; YANG, FEI; ZHU, PENG. EIGENVALUES OF GEOMETRIC OPERATORS RELATED TO THE WITTEN LAPLACIAN UNDER THE RICCI FLOW. Glasgow mathematical journal, Tome 59 (2017) no. 3, pp. 743-751. doi: 10.1017/S0017089516000537
@article{10_1017_S0017089516000537,
     author = {FANG, SHOUWEN and YANG, FEI and ZHU, PENG},
     title = {EIGENVALUES {OF} {GEOMETRIC} {OPERATORS} {RELATED} {TO} {THE} {WITTEN} {LAPLACIAN} {UNDER} {THE} {RICCI} {FLOW}},
     journal = {Glasgow mathematical journal},
     pages = {743--751},
     year = {2017},
     volume = {59},
     number = {3},
     doi = {10.1017/S0017089516000537},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000537/}
}
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