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Distinguished connections on (J2 = ±1)-metric manifolds

Abstract: 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 (J2 = ±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 connections, named canonical connections, thus extending to almost Norden and almost product Riemannian manifolds the families introduced in almost Hermitian and almost para-Hermitian manifolds in [13] and [18]. We also prove that every connection studied in this paper is a canonical connection, when it exists and it is an adapted connection. © 2016, Masarykova Universita. All rights reserved.

 Fuente: Archivum Mathematicum, 2016, 52, 159?203

 Editorial: Masarykova Universita

 Año de publicación: 2016

 Nº de páginas: 45

 Tipo de publicación: Artículo de Revista

 DOI: 10.5817/AM2016-3-159

 ISSN: 0044-8753,1212-5059

 Url de la publicación: https://doi.org/10.5817/AM2016-3-159