(1, 2)-Symplectic Structures, nearly Kahler Structures and S6

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Authors

  • International Centre for Theoretical Physics, Trieste ,IT

Abstract

The exact relations between the Hermitian, the Symplectic and the Nearly Kahler Structures are established. The standard complex structure Js on SO(2n + l)/U(n) is shown to be the same as the almost complex structure J1(one of the canonical almost complex structure on SO(2n+l)/U(n) considered as a twistor space over (S2n, g0)). A corollary is that S6 does not allow any complex structure orthogonal to the standard metric g0. On an almost complex manifold with an arbitrary metric a (1, 2)-tensor A is defined. If A is closed as a vector valued 2-form, then it is proved that constant sectional curvature implies zero curvature. This is related to Hsiung's work, which is discussed at the end.

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Published

1994-12-01

How to Cite

Datta, B. (1994). (1, 2)-Symplectic Structures, nearly Kahler Structures and S<sup>6</sup>. The Journal of the Indian Mathematical Society, 60(1-4), 171–190. Retrieved from https://www.informaticsjournals.com/index.php/jims/article/view/21964