Geodesic
Infinitesimal Isometries on Compact Manifolds
Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 461-464

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Let X denote a non-vanishing infinitesimal isometry on a compact Riemannian manifold Mn . Let denote the deRham complex of M. We write i(X) for the operator of interior product, and L(X) the Lie derivative on the elements of A(M). We define E(M) = {u ∈ A(M)| i(X)u = 0, L(X)u= 0}. 
Liang, Chao-Chu. Infinitesimal Isometries on Compact Manifolds. Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 461-464. doi: 10.4153/CMB-1980-069-x
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     title = {Infinitesimal {Isometries} on {Compact} {Manifolds}},
     journal = {Canadian mathematical bulletin},
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     year = {1980},
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     number = {4},
     doi = {10.4153/CMB-1980-069-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-069-x/}
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