CONSTRCUTION OF WARPED-LIKE PRODUCT MANIFOLDS WITH SPIN(7) HOLONOMY

E. Cartan gave the holonomy group definition and the classification of irreducible, simply-connected and symmetric manifolds in 1925. In 1955, Marcel Berger gave the holonomy group classification list of irreducible, simplyconnected and non-symmetric manifolds [6]. Berger’s holonomy group list called the Berger list is short and includes two exceptional cases, G2 holonomy on a 7-dimensional manifold and Spin(7) holonomy on an 8-manifold. These holonomy groups are called the exceptional holonomy groups and manifolds with these holonomy groups are called the exceptional holonomy manifolds. When M. Berger gave the possible holonomy groups list, he did not know whether G2 and Spin(7) holonomy groups manifolds exist or not. In 1987, the existence question of exceptional holonomy manifolds was answered [1]. R. Bryant and S. Salomon gave the first complete example of Spin(7) holonomy manifold which was the total space of the spin bundle over the 4-sphere [2]. Dominic Joyce gave the first compact examples of exceptional holonomy manifolds in 1996 and wrote the methods of construction of manifolds as a book in [3]. He constructed manifold examples by resolving the singularities of the orbifold T /Γ for some groups Γ. ∗E-mail Address: uguzs@itu.edu.tr (S. Uguz), Tel.: +90-212-2856795; fax:+90-2122856386.