G-structures defined by tensor fields of electromagnetic type

Spaces of constant para-holomorphic sectional curvature

“…[3], [11]) is a pseudo-Riemannian manifold (M n ,g) together with a (1,1) tensor field / such that J 4 = 1 and whose characteristic polynomial is (x -iY ι {x + lY 2 (x 2 + l) s with r x + r 2 + 2s = n\ also, the tensor fields g and / are related by one of the following relations:…”

Real hypersurfaces of $e$-$(J^4=1)$-Kaehler manifolds

“…Introduction (J 4 = 1)-Kaehler manifolds were introduced in [3] as a natural generalization of both Kaehler manifolds and para-Kaehler manifolds. Several interesting results on the topic can be found in [3][4][5]7].…”

Structures of electromagnetic type on vector bundles

“…It is proved ( [7]) that the G-structure defined by J above is also defined by a tensor field, say again J, satisfying (J 2 − 1)(J 2 + 1) = 0, that is, the relation J 4 = 1 considered in the present paper.…”

“…In the 4-dimensional case the group reduces to G = GL(1, R) × GL(1, R) × GL(1, C). It is also proved ( [7]) that there exists an adapted Riemannian metric so that the group can be reduced to G = O(r 1 ) × O(r 2 ) × U (s), and in the 4-dimensional case to Z 2 × Z 2 × U (1), that is, essentially to the unitary group U (1).…”