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The main goal of this paper is to extend the so-called Dirac-FrenkelVariational Principle in the framework of tensor Banach spaces. To this end weobserve that a tensor product of normed spaces can be described as a union ofdisjoint connected components. Then we show that each of these connectedcomponents, composed by tensors in Tucker format with a fixed rank, is a Banachmanifold modelled in a particular Banach space, for which we provide localcharts. The description of the local charts of these manifolds is crucial foran algorithmic treatment of high-dimensional partial differential equations andminimization problems. In order to describe the relationship between thesemanifolds and the natural ambient space we prove under natural conditions thateach connected component can be immersed in a particular ambient Banach space.This fact allows us to finally extend the Dirac-Frenkel variational principlein the framework of topological tensor spaces.

On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces