Publication detail

Geometry of almost Cliffordian manifolds: classes of subordinated connections

HRDINA, J. VAŠÍK, P.

Czech title

Geometrie skoro Cliffordovských variet: třídy podkladových konexí

English title

Geometry of almost Cliffordian manifolds: classes of subordinated connections

Type

journal article in Web of Science

Language

en

Original 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.

Czech abstract

Dokázali jsme, že na skoro Cliffordovských varietách založených na O existuje třída podkladových konexí a popsali jsme je.

English 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 in English

Clifford algebra, affinor structure, G--structure, linear connection, planar curves

RIV year

2014

Released

08.01.2014

ISSN

1300-0098

Volume

38

Number

1

Pages from–to

179–190

Pages count

12

BIBTEX


@article{BUT104924,
  author="Jaroslav {Hrdina} and Petr {Vašík},
  title="Geometry of almost Cliffordian manifolds: classes of subordinated connections",
  year="2014",
  volume="38",
  number="1",
  month="January",
  pages="179--190",
  issn="1300-0098"
}