Two new families of Finsler connections on even-dimensional manifolds

zbMATH Open1350.53096arXiv1305.5996MaRDI QIDQ2820179

Hamid Reza Salimi Moghaddam

Publication date: 14 September 2016

Published in: International Electronic Journal of Geometry (Search for Journal in Brave)

Abstract: Let $F^{2n}=(M,M^{\prime },F^{ast})$ be an even-dimensional pseudo-Finsler manifold. We construct an almost hypercomplex structure on any chart domain of a certain atlas of $M^{\prime }$ by using a considered non-linear connection. Then by using the almost hypercomplex structure we define two new families of Finsler connections. Also we show that for any Finsler connection $abla$ there exists a linear connection $D$ such that the local almost hypercomplex structure is parallel with respect to it.

Full work available at URL: https://arxiv.org/abs/1305.5996

zbMATH Keywords

almost hypercomplex structurenonlinear connectionFinsler connectionpseudo-Finsler manifold

Mathematics Subject Classification ID

General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Local differential geometry of Finsler spaces and generalizations (areal metrics) (53B40) Linear and affine connections (53B05)

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