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Papers - Old and New Structures on Products of Spheres Old and New Structures on Products of Spheres Abstract A classical theorem of Kervaire states that products of spheres are parallelizable if and only if at least one of the factors has odd dimension. In this note I give explicit parallelizations, and use them to describe G-structures on products of two spheres, for G=U(n), Sp(n), G2, Spin(7), Spin(9). This approach gives an alternative description of the classical Calabi-Eckmann structures, and of some G2, Spin(7), Spin(9)-structures on S6×S1, S7×S1, S15×S1 respectively. In other products of spheres some new G-structures are obtained.

Introduction Papers Families of strong KT structures in six dimensions Locally conformal Kähler reduction Structures related to parallelizations Strutture hermitiane e speciali su prodotti di sfere Old and New Structures on Products of Spheres An explicit parallelization on products of spheres Hopf surfaces: locally conformal Kähler metrics and foliations Hermitian and special structures on products of spheres