Eigenvalues of vector fields,Bott's residue formula and integral invariants |
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Institution: | Department of Mathematics, Tongji University, Shanghai 200092, China |
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Abstract: | Given a compatible vector field on a compact connected almost-complex manifold, we show in this article that the multiplicities of eigenvalues among the zero point set of this vector field have intimate relations. We highlight a special case of our result and reinterpret it as a vanishing-type result in the framework of the celebrated Atiyah–Bott–Singer localization formula. This new point of view, via the Chern–Weil theory and a strengthened version of Bott's residue formula, can lead to an obstruction to Killing real holomorphic vector fields on compact Hermitian manifolds in terms of a curvature integral. |
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Keywords: | Vector field Eigenvalue Atiyah–Bott–Singer localization formula Bott's residue formula Integral invariant |
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