On the geometry of almost Golden Riemannian manifolds

Abstract

An almost Golden Riemannian structure $(\phi ,g)$ on a manifold is given by a tensor field $\phi$ of type (1,1) satisfying the Golden section relation ${\phi }^2=\phi +1$, and a pure Riemannian metric $g$, i.e., a metric satisfying $g(\phi X,Y)=g(X,\phi Y)$. We study connections adapted to such a structure, finding two of them, the first canonical and the well adapted, which measure the integrability of $\phi$ and the integrability of the $G$-structure corresponding to $(\phi ,g)$.

References in corpus (2)

• Distinguished connections on $(J^2=\pm 1)$-metric manifolds
• The well adapted connection of a $(J^2=\pm 1)$-metric manifold

Cited by in corpus (1)

• Slant and semi-slant submanifolds in metallic Riemannian manifolds