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Papers - Hermitian and special structures on products of spheres | |
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This is my PhD thesis, discussed on 2001, April 27th, at
University of Pisa, Italy.
Abstract
In the first chapter I describe a family of locally conformal Kähler metrics
on class 1 Hopf surfaces, and study in details a 2-dimensional foliation
arising from this family.
In the remaining chapters, I start from
a classical theorem of Kervaire stating that products of spheres are
parallelizable if and only if at least one of the factors has odd
dimension to give explicit parallelizations, and then use these parallelizations
to obtain G-structures on Sm×Sn,
where G=U(m+n)/2, Sp(m+n)/4, G2, Spin(7), Spin(9).
In particular, it is shown that Calabi-Eckmann Hermitian structures
on products of two odd-dimensional spheres are invariant with respect to
these parallelizations.
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