ΕΡΜΙΤΙΑΝΗ ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ ΣΕ /Α-ΔΕΣΜΕΣ

IN THIS WORK, WE FIRST DEVELOP METHODS OF DIFFERENTIATION SUITABLE FOR MAPPINGS BETWEEN TOPOLOGICAL A-MODULES, WHERE A IS A COMMUTATIVE LOCALLY M-CONVEX * -ALGEBRA WITH UNIT. THIS EXTENDS WELL-KNOWN METHODS OF DIFFERENTIATION ON TOPOLOGICAL VECTOR SPACES, SUCH AS FRECHET AND HYERS DIFFERENTIATION. APPLYING THE ABOVE DIFFERENTIAL CALCULUS, WE INTRODUCE THE CONCEPT OF DIFFERENTIABLE A-MANIFOLDS, THAT IS, DIFFERENTIABLE MANIFOLDS MODELLED ON TOPOLOGICAL (FINITELY GENERATED AND PROJECTIVE) A-MODULES. WE ALSO EXAMINE BASIC PROPERTIES OF THE RESPECTIVE TANGENT SPACES, DERIVATIONS AND VECTOR FIELDS. FINALLY, WE STUDY DIFFERENTIABLE BUNDLES OF FIBRE TYPE A TOPOLOGICAL A-MODULE AND PROVE THAT SUCH BUNDLES ARE PROVIDED WITH A DIFFERENTIABLE A- HERMITIAN STRUCTURE AND A COMPATIBLECONNECTION.

Grantor dc:publisher

National and Kapodistrian University of Athens

Year dc:date

1986

Author dc:creator

• Παπατριανταφύλλου, Μαρία

• ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ/ΟΛΙΚΗ ΑΝΑΛΥΣΗ
• ΔΙΑΦΟΡΙΣΙΜΕΣ /Α-ΔΕΣΜΕΣ
• ΔΙΑΦΟΡΙΣΙΜΕΣ /Α-ΠΟΛΛΑΠΛΟΤΗΤΕΣ
• Μαθηματικά
• ΤΟΠΟΛΟΓΙΚΗ ΑΛΓΕΒΡΑ
• DEFFERENTIABLE /A-MANIFOLDS
• TOPOLOGICAL ALGEBRA
• Φυσικές Επιστήμες
• Natural Sciences
• Mathematics

Language dc:language

gre

Identifier

10.12681/eadd/0132

OAI identifier oai:identifier

oai:10442/0132