Geometry of almost Cliffordian manifolds: classes of subordinated connections

Authors : Jaroslav HRDINA, Petr VASÍK

Pages : 179-190

Doi:10.3906/mat-1206-40

View : 22 | Download : 4

Publication Date : 0000-00-00

Article Type : Research Paper

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 insert ignore into journalissuearticles values(s,t); is given by a reduction of the structure group GLinsert ignore into journalissuearticles values(km, R); to GLinsert ignore into journalissuearticles values(m, O);, where k=2s+t and m \in N. An almost Cliffordian manifold is given by a reduction of the structure group to GLinsert ignore into journalissuearticles values(m, O); GLinsert ignore into journalissuearticles values(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