Complex Structures on some Stiefel Manifolds
Differential Geometry
2007-05-23 v1
Abstract
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).
Cite
@article{arxiv.math/0008213,
title = {Complex Structures on some Stiefel Manifolds},
author = {Liviu Ornea and Paolo Piccinni},
journal= {arXiv preprint arXiv:math/0008213},
year = {2007}
}
Comments
LaTex, 11 pages, to be published in Bull. Soc. Sc. Math. Roumanie, Volume in memory of G. Vranceanu