Spin (7)-structures in principal fibre bundles over Riemannian manifolds withG 2-structure
- 40 Downloads
We consider principal fibre bundles with one-dimensional fiber over manifolds withG 2-structure. We define twoSpin(7)-structures on the total bundle space and find relations between the respective structures on the total space and the base. Finally we construct examples ofSpin(7)-structures using the results previously proved.
1991 Mathematics Subject Classification53C10 53C21 55R10
Unable to display preview. Download preview PDF.
- [C1] Cabrera F. M.,On Riemannian manifolds with G 2-structure, Bollettino U.M.I., to appear.Google Scholar
- [C2] Cabrera F. M.,On Riemannian manifolds with Spin(7)-structure, Publ. Math. Dehecen, to appear.Google Scholar
- [CMS] Cabrera F. M., Monar M. D., Swann A. F.,Classification of G 2-structures, J. Lond. Math. Soc., to appear.Google Scholar
- [Gr1] Gray A.,Some examples of almost Hermitian manifolds, Ill. J. Math.,10 (1969), 353–366.Google Scholar
- [Gr3] Gray A.,Vector cross products, Rend. Sem. Mat. Univ. Politec. Torino,35 (1976–77), 69–75.Google Scholar
- [J] Joyce D.,Compact Riemannian 7-manifolds with holonomy G 2, I and II, J. Diff. Geom., to appear.Google Scholar
- [Ko] Kostant B.,Quantization and unitary representations, Lecture Notes in Math., Soc.,170, Springer-Verlag, Berlin and New York (1970), 87–207.Google Scholar
- [Z] Zvengrowski A.,A 3-fold vector cross product in IR8, Comment Math. Helv.40, 216–231.Google Scholar