Derivations and Linear Connections on Clifford Vector Bundles

Derivations and Linear Connections on Clifford Vector Bundles The goal of this article is to introduce a concept of Clifford structures on vector bundles as natural extensions of the standard complex and quaternionic structures, and to determine the derivations and linear connections on smooth Clifford vector bundles compatible with their Clifford structures. The basic object used to get such descriptions is an involution on the space of derivations of a Clifford vector bundle explicitly defined in terms of the specific Clifford structure. That involution is actually derived from an operation called the Clifford conjugation relative to a Clifford structure, which is defined in a purely algebraic setting as an involution on the space of derivations of a Euclidean Clifford algebra. Its definition essentially relies on the use and a complete description of the geometric concept of tangent Clifford structures of a Euclidean Clifford algebra. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Applied Clifford Algebras Springer Journals

Derivations and Linear Connections on Clifford Vector Bundles

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Physics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Applications of Mathematics; Physics, general
ISSN
0188-7009
eISSN
1661-4909
D.O.I.
10.1007/s00006-017-0767-1
Publisher site
See Article on Publisher Site

Abstract

The goal of this article is to introduce a concept of Clifford structures on vector bundles as natural extensions of the standard complex and quaternionic structures, and to determine the derivations and linear connections on smooth Clifford vector bundles compatible with their Clifford structures. The basic object used to get such descriptions is an involution on the space of derivations of a Clifford vector bundle explicitly defined in terms of the specific Clifford structure. That involution is actually derived from an operation called the Clifford conjugation relative to a Clifford structure, which is defined in a purely algebraic setting as an involution on the space of derivations of a Euclidean Clifford algebra. Its definition essentially relies on the use and a complete description of the geometric concept of tangent Clifford structures of a Euclidean Clifford algebra.

Journal

Advances in Applied Clifford AlgebrasSpringer Journals

Published: Mar 3, 2017

References

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