Year: 2005
Type: preprint
Abstract: This paper, the third in a series of eight introduces some of the basic concepts of the theory of extensors needed for our formulation of the differential geometry of smooth manifolds . Key notions such as the extension and generalization operators of a given linear operator (a (1,1)-extensor) acting on a real vector space V are introduced and studied in details. Also, we introduce the notion of the determinant of a (1,1)-extensor and the concepts of standard and metric Hodge (star) operators, disclosing a non trivial and useful relation between them.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1895578181