Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 25, No 1, (1999), 83p-90p
Abstract:
It is shown that the spheres S^(2n) (resp: S^k with k ≡ 1 mod 4)
can be given neither an indefinite metric of any signature (resp: of signature
(r, k − r) with 2 ≤ r ≤ k − 2) nor an almost paracomplex structure. Further
for every given Riemannian metric on an almost para-Hermitian manifold
with the associated 2-form φ one can construct an almost Hermitian structure
(under certain conditions, two different almost Hermitian structures)
whose associated 2-form(s) is φ.
