- Turkish Journal of Mathematics
- Vol: 38 Issue: 1
- Geometry of almost Cliffordian manifolds: classes of subordinated connections
Geometry of almost Cliffordian manifolds: classes of subordinated connections
Authors : Jaroslav Hrdina, Petr Vasík
Pages : 179-190
Doi:10.3906/mat-1206-40
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :An almost Clifford and an almost Cliffordian manifold is a G--structure based on the definition of Clifford algebras. An almost Clifford manifold based on O:= Cl (s,t) is given by a reduction of the structure group GL(km, R) to GL(m, O), where k=2s+t and m \in N. An almost Cliffordian manifold is given by a reduction of the structure group to GL(m, O) GL(1, O). We prove that an almost Clifford manifold based on O is such that there exists a unique subordinated connection, while the case of an almost Cliffordian manifold based on O is more rich. A class of distinguished connections in this case is described explicitly.Keywords : Clifford algebra, affinor structure, G--structure, linear connection, planar curves