Publication result detail

Geometry of almost Cliffordian manifolds: classes of subordinated connections

HRDINA, J.; VAŠÍK, P.

Original Title

Geometry of almost Cliffordian manifolds: classes of subordinated connections

English Title

Geometry of almost Cliffordian manifolds: classes of subordinated connections

Type

WoS Article

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.

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

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

Key words in English

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

Authors

HRDINA, J.; VAŠÍK, P.

RIV year

2015

Released

08.01.2014

ISBN

1300-0098

Periodical

TURKISH JOURNAL OF MATHEMATICS

Volume

38

Number

1

State

Republic of Turkey

Pages from

179

Pages to

190

Pages count

12

BibTex

@article{BUT104924,
  author="Jaroslav {Hrdina} and Petr {Vašík}",
  title="Geometry of almost Cliffordian manifolds: classes of subordinated connections",
  journal="TURKISH JOURNAL OF MATHEMATICS",
  year="2014",
  volume="38",
  number="1",
  pages="179--190",
  doi="10.3906/mat-1206-40",
  issn="1300-0098"
}