Transversal Twistor Spaces of Foliations |
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| Authors: | Izu Vaisman |
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| Institution: | (1) Department of Mathematics, University of Haifa, Mount Carmel, 31905 Haifa, Israel |
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| Abstract: | The transversal twistor space of a foliation
of an even codimension is the bundle
of the complex structures of the fibers of the transversalbundle of
. On
there exists a foliation
by covering spaces of the leaves of
, and any Bottconnection of
produces an ordered pair
of transversal almost complex structures of
. The existence of a Bott connection which yields a structure
1 that is projectable to the space of leaves isequivalent to the fact that
is a transversallyprojective foliation. A Bott connection which yields a projectablestructure
2 exists iff
isa transversally projective foliation which satisfies a supplementarycohomological condition, and, in this case,
1is projectable as well.
2 is never integrable.The essential integrability condition of
1 isthe flatness of the transversal projective structure of
. |
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| Keywords: | foliated (projectable) objects foliations transversal twistor spaces |
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