Foliations induced by metallic structures

2019/03/10 by Blaga, Adara M., Nannicini, Antonella
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.04006

Abstract

We give necessary and sufficient conditions for the real distributions defined by a metallic pseudo-Riemannian structure to be integrable and geodesically invariant, in terms of associated tensor fields to the metallic structures and of adapted connections. In the integrable case, we prove a Chen-type inequality for these distributions and provide conditions for a metallic map to preserve these distributions. If the structure is metallic Norden, we describe the complex metallic distributions in the same spirit.

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