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.
Foliations induced by metallic structures / Antonella Nannicini; Adara Monica Blaga. - In: NEW YORK JOURNAL OF MATHEMATICS. - ISSN 1076-9803. - STAMPA. - 29:(2023), pp. 771-791.
Foliations induced by metallic structures
Antonella Nannicini;
2023
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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.