Almost Poly-Norden Manifolds

Abstract

We introduce a new kind of manifold, namely poly-Norden manifolds. We show that this class includes Norden manifolds, spheres and Euclidean $n-$ space as examples. We investigate certain geometric properties of such manifolds and show that a holomorphic-like map between such manifolds are harmonic under some conditions. We also investigate constancy of certain maps between poly-Norden manifolds and other manifolds endowed with differential structures.