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We discuss the decomposition of degree two basic cohomology for codimension four taut Riemannian foliation according to the holonomy invariant transversal almost complex structure $J$, and show that $J$ is $C^{\infty}$ pure and full. In addition, we obtain an estimate of the dimension of basic $J$-anti-invariant subgroup. These are the foliated version for the corresponding results of T. Draghici et al.~\cite{DLZ}.
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참고문헌 (10)
참고문헌 신청
D. Dominguez / 1998 / Finiteness and tenseness theorems for Riemannian foliations / Amer. J. Math 120(6):1237~1276
S. K. Donaldson / 2006 / Inspired by S. S. Chern / World Sci. Publ :153~172
T. Draghici / 2010 / Symplectic forms and cohomology decomposition of almost complex four-manifolds / Int. Math. Res. Not. IMRN 2010(1):1~17
Anna Fino / 2010 / On Some Cohomological Properties of Almost Complex Manifolds / Journal of Geometric Analysis 20(1):107~131
F. W. Kamber / 1983 / Differential geometry / Birkhauser :103~152
S. K. Donaldson / 2006 / Inspired by S. S. Chern / World Sci. Publ :153~172
T. Draghici / 2010 / Symplectic forms and cohomology decomposition of almost complex four-manifolds / Int. Math. Res. Not. IMRN 2010(1):1~17
Anna Fino / 2010 / On Some Cohomological Properties of Almost Complex Manifolds / Journal of Geometric Analysis 20(1):107~131
F. W. Kamber / 1983 / Differential geometry / Birkhauser :103~152
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