Adara M. Blaga [a] and Antonella Nannicini [b]
On the geometry of metallic pseudo-Riemannian structures
Received: 19 December 2018
Accepted: 26 June 2019
Mathematics Subject Classification (2010): 53C15, 53C25.
Keywords: Metallic pseudo-Riemannian structures, natural connection, Norden structures.
[a]: West University of Timişoara, Department of Mathematics, Bld. V. Pârvan nr. 4, 300223, Timişoara, România
[b]: University of Florence, Department of Mathematics and Informatics "U. Dini", Viale Morgagni 67/a, 50134, Firenze, Italy
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Abstract: We generalize the notion of metallic structure in the pseudo-Riemannian setting, define the metallic Norden structure and study its integrability. We consider metallic maps between metallic manifolds and give conditions under which they are constant. We also construct a metallic natural connection recovering as particular case the Ganchev and Mihova connection, which we extend to a metallic natural connection on the generalized tangent bundle. Moreover, we construct metallic pseudo-Riemannian structures on the tangent and cotangent bundles.