F(a0, a1, ...., an)-structures on manifolds

Abstract

The aim of the present paper is to study the geometry of n-dimensional
differentiable manifolds endowed with F(a0, a1, ...., an)-structure satisfying
anFn +an-1Fn-1+.......+a1F+a0I = 0 and establish its existence. Also, it is
proved that for the complex numbers, the dimension of a manifold M endowed
with F(a0, a1, ...., an)-structure is even. Furthermore, we study the Nijenhuis
tensor of a tensor field F of type (1,1) satisfying the general quadratic equation, which is a particular case of the F(a0, a1, ......, an)-structure. At last, we study the integrability conditions of an F(a0, a1, ......, an)-structure.