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Distinguished connections on ( J 2 = ± 1 ) -metric manifolds

Fernando EtayoRafael Santamaría — 2016

Archivum Mathematicum

We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of ( J 2 = ± 1 ) -metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among connections. We prove that the first canonical and the well adapted connections define a one-parameter family of adapted...

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