For a Spin(9)-structure on a Riemannian manifold M (16) we write explicitly the matrix psi of its Kahler 2-forms and the canonical 8-form Phi(Spin(9)). We then prove that Phi(Spin(9)) coincides up to a constant with the fourth coefficient of the characteristic polynomial of psi. This is inspired by lower dimensional situations, related to Hopf fibrations and to Spin(7). As applications, formulas are deduced for Pontrjagin classes and integrals of Phi(Spin(9)) and Phi(Spin)(9) in the special case of holonomy Spin(9).
Spin(9) and almost complex structures on 16-dimensional manifolds / Maurizio, Parton; Piccinni, Paolo. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - STAMPA. - 41:3(2012), pp. 321-345. [10.1007/s10455-011-9285-x]
Spin(9) and almost complex structures on 16-dimensional manifolds
PICCINNI, Paolo
2012
Abstract
For a Spin(9)-structure on a Riemannian manifold M (16) we write explicitly the matrix psi of its Kahler 2-forms and the canonical 8-form Phi(Spin(9)). We then prove that Phi(Spin(9)) coincides up to a constant with the fourth coefficient of the characteristic polynomial of psi. This is inspired by lower dimensional situations, related to Hopf fibrations and to Spin(7). As applications, formulas are deduced for Pontrjagin classes and integrals of Phi(Spin(9)) and Phi(Spin)(9) in the special case of holonomy Spin(9).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
