Complex Structures on some Stiefel Manifolds

Details Complex Structures on some Stiefel Manifolds Complex Structures on some Stiefel Manifolds

2000-08-29

arxiv.org/abs/math/0008213v1

Mathematics

Differential Geometry

LaTex, 11 pages, to be published in Bull. Soc. Sc. Math. Roumanie, Volume in memory of G. Vranceanu

Scientific paper

We discuss conditions for the integrability of an almost complex structure defined on the total space of an induced Hopf S^3-bundle over a Sasakian manifold . As an application, we obtain an uncountable family of inequivalent complex structures on the Stiefel manifolds of orthonormal 2-frames in C^{n+1}, non compatible with its standard hypercomplex structure. Similar families of complex structures are constructed on the Stiefel manifold of oriented orthonormal 4-frames in R^{n+1}, as well as on some special Stiefel manifolds related to the groups G_2 and Spin(7).

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