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  and . 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. T. 52 (2016), 159–203
Editorial: Masarykova Universita
Año de publicación: 2016
Nº de páginas: 45
Tipo de publicación: Artículo de Revista
Url de la publicación: https://doi.org/10.5817/AM2016-3-159