Harmonic two-forms on manifolds with non-negative isotropic curvature |
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Authors: | Peng Zhu |
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Institution: | (1) Centro de Investigaci?n en Matem?ticas (CIMAT), A.P. 402, Guanajuato, 36000, Gto., Mexico;(2) FaMAF-CIEM, Ciudad Universitaria, Cordoba, 5000, Argentina; |
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Abstract: | We prove that L
2 harmonic two-forms are parallel if a complete manifold (M, g) has the non-negative isotropic curvature. Furthermore, if (M, g) has positive isotropic curvature at some point, then there is no non-trivial L
2 harmonic two-form. We obtain that an almost K?hler manifold of non-negative isotropic curvature is K?hler and a symplectic
manifold can not admit any almost K?hler structure of positive isotropic curvature. |
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Keywords: | |
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