Vector Fields Orthogonal to a Nonvanishing Infinitesimal Isometry

Chao-Chu Liang
1979 Proceedings of the American Mathematical Society  
Let A be a nonvanishing infinitesimal isometry on a compact Riemannian manifold M. If there exists a nonvanishing vector field orthogonal to X and commuting with X, then the Euler characteristic of the complex consisting of all the differential forms u satisfying i(X)u -0 -L(x)u is zero. Let A denote a nonvanishing infinitesimal isometry on a compact Riemannian manifold M". Let A(M) = {Ak(M), d)0<k<n denote the de Rham complex of M. We let /(A) denote the interior product operator, and L(A) the
more » ... rator, and L(A) the Lie derivative on the elements of A(M). We define E(M) = {u E A(M)\i(X)u = 0 = L(X)u). The cohomology of the complex {E(M), d) can
doi:10.2307/2042766 fatcat:fucnw5kpdrcpbd627zfwo2kp5q