{"id":{"repo_id":"greece","oai_identifier":"oai:10442/0132"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/0132","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΕΡΜΙΤΙΑΝΗ ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ ΣΕ /Α-ΔΕΣΜΕΣ","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Παπατριανταφύλλου, Μαρία"],"institution":"National and Kapodistrian University of Athens","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1986,"date_issued":"1986","date_published":"1986","updated_at":"2026-07-24T02:24:52Z","subjects":["ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ/ΟΛΙΚΗ ΑΝΑΛΥΣΗ","ΔΙΑΦΟΡΙΣΙΜΕΣ /Α-ΔΕΣΜΕΣ","ΔΙΑΦΟΡΙΣΙΜΕΣ /Α-ΠΟΛΛΑΠΛΟΤΗΤΕΣ","Μαθηματικά","ΤΟΠΟΛΟΓΙΚΗ ΑΛΓΕΒΡΑ","DEFFERENTIABLE /A-MANIFOLDS","TOPOLOGICAL ALGEBRA","Φυσικές Επιστήμες","Natural Sciences","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/0132"],"render_values":[{"text":"10.12681/eadd/0132","href":"https://doi.org/10.12681/eadd/0132","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/0132","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Παπατριανταφύλλου, Μαρία"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1986"]},{"key":"dc:publisher","label":"Institution","values":["National and Kapodistrian University of Athens","Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ/ΟΛΙΚΗ ΑΝΑΛΥΣΗ","ΔΙΑΦΟΡΙΣΙΜΕΣ /Α-ΔΕΣΜΕΣ","ΔΙΑΦΟΡΙΣΙΜΕΣ /Α-ΠΟΛΛΑΠΛΟΤΗΤΕΣ","Μαθηματικά","ΤΟΠΟΛΟΓΙΚΗ ΑΛΓΕΒΡΑ","DEFFERENTIABLE /A-MANIFOLDS","TOPOLOGICAL ALGEBRA","Φυσικές Επιστήμες","Natural Sciences","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["gre"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/0132","http://hdl.handle.net/10442/hedi/0132"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","ΣΤΗΝ ΕΡΓΑΣΙΑ ΑΥΤΗ ΑΝΑΠΤΥΣΟΥΜΕ, ΑΡΧΙΚΑ, ΜΕΘΟΔΟΥΣ ΔΙΑΦΟΡΙΣΗΣ ΓΙΑ ΑΠΕΙΚΟΝΙΣΕΙΣ ΜΕΤΑΞΥ ΤΟΠΟΛΟΓΙΚΩΝ Α-ΠΡΟΤΥΠΩΝ, ΟΠΟΥ Α ΕΙΝΑΙ ΜΙΑ ΜΕΤΑΘΕΤΙΚΗ ΤΟΠΙΚΑ Μ-ΚΥΡΤΗ * -ΑΛΓΕΒΡΑ ΜΕ ΜΟΝΑΔΑ. ΟΙ ΠΡΟΗΓΟΥΜΕΝΕΣ ΜΕΘΟΔΟΙ ΕΠΕΚΤΕΙΝΟΥΝ ΓΝΩΣΤΕΣ ΔΙΑΦΟΡΙΣΕΙΣ ΤΩΝ ΤΟΠΟΛΟΓΙΚΩΝ ΔΙΑΝΥΣΜΑΤΙΚΩΝ ΧΩΡΩΝ, Λ.Χ. ΤΙΣ ΔΙΑΦΟΡΙΣΕΙΣ FRECHET ΚΑΙ HYERS. ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΟΝ ΠΑΡΑΠΑΝΩ ΔΙΑΦΟΡΙΚΟ ΛΟΓΙΣΜΟ, ΕΙΣΑΓΟΥΜΕ ΤΗΝ ΕΝΝΟΙΑ ΤΩΝ ΔΙΑΦΟΡΙΣΙΜΩΝΑ- ΠΟΛΛΑΠΛΟΤΗΤΩΝ, ΔΗΛΑΔΗ ΤΩΝ ΔΙΑΦΟΡΙΣΙΜΩΝ ΠΟΛΛΑΠΛΟΤΗΤΩΝ ΜΕ ΜΟΝΤΕΛΑ ΤΟΠΟΛΟΓΙΚΑ(ΠΕΠΕΡΑΣΜΕΝΩΣ ΠΑΡΑΓΟΜΕΝΑ ΚΑΙ ΠΡΟΒΟΛΙΚΑ) Α-ΠΡΟΤΥΠΑ. ΕΠΙΣΗΣ ΕΞΕΤΑΖΟΥΜΕ ΒΑΣΙΚΕΣ ΙΔΙΟΤΗΤΕΣ ΤΩΝ ΑΝΤΙΣΤΟΙΧΩΝ ΕΦΑΠΤΟΜΕΝΩΝ ΧΩΡΩΝ ΠΑΡΑΓΩΓΙΣΕΩΝ ΚΑΙ ΔΙΑΝΥΣΜΑΤΙΚΩΝ ΠΕΔΙΩΝ. ΤΕΛΟΣ ΜΕΛΕΤΑΜΕ ΤΙΣ ΔΙΑΦΟΡΙΣΙΜΕΣ ΔΕΣΜΕΣ ΜΕ ΝΗΜΑΤΑ ΤΟΠΟΛΟΓΙΚΑ Α-ΠΡΟΤΥΠΑ ΚΑΙΑΠΟΔΕΙΚΝΥΟΥΜΕ ΟΤΙ ΟΙ ΠΑΡΑΠΑΝΩ ΔΕΣΜΕΣ ΕΦΟΔΙΑΖΟΝΤΑΙ ΜΕ ΔΙΑΦΟΡΙΣΙΜΗ Α-ΕΡΜΙΤΙΑΝΗ ΔΟΜΗ ΚΑΙ ΣΥΜΒΙΒΑΣΤΗ ΣΥΝΟΧΗ."]},{"key":"dc:title","label":"Title","values":["ΕΡΜΙΤΙΑΝΗ ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ ΣΕ /Α-ΔΕΣΜΕΣ","HERMITIAN DIFFERENTIAL GEOMETRY ON /A-BUNDLES"]}]}],"canonical_facts":{"dc:creator":["Παπατριανταφύλλου, Μαρία"],"dc:date":["1986"],"dc:description":["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.","ΣΤΗΝ ΕΡΓΑΣΙΑ ΑΥΤΗ ΑΝΑΠΤΥΣΟΥΜΕ, ΑΡΧΙΚΑ, ΜΕΘΟΔΟΥΣ ΔΙΑΦΟΡΙΣΗΣ ΓΙΑ ΑΠΕΙΚΟΝΙΣΕΙΣ ΜΕΤΑΞΥ ΤΟΠΟΛΟΓΙΚΩΝ Α-ΠΡΟΤΥΠΩΝ, ΟΠΟΥ Α ΕΙΝΑΙ ΜΙΑ ΜΕΤΑΘΕΤΙΚΗ ΤΟΠΙΚΑ Μ-ΚΥΡΤΗ * -ΑΛΓΕΒΡΑ ΜΕ ΜΟΝΑΔΑ. ΟΙ ΠΡΟΗΓΟΥΜΕΝΕΣ ΜΕΘΟΔΟΙ ΕΠΕΚΤΕΙΝΟΥΝ ΓΝΩΣΤΕΣ ΔΙΑΦΟΡΙΣΕΙΣ ΤΩΝ ΤΟΠΟΛΟΓΙΚΩΝ ΔΙΑΝΥΣΜΑΤΙΚΩΝ ΧΩΡΩΝ, Λ.Χ. ΤΙΣ ΔΙΑΦΟΡΙΣΕΙΣ FRECHET ΚΑΙ HYERS. ΧΡΗΣΙΜΟΠΟΙΩΝΤΑΣ ΤΟΝ ΠΑΡΑΠΑΝΩ ΔΙΑΦΟΡΙΚΟ ΛΟΓΙΣΜΟ, ΕΙΣΑΓΟΥΜΕ ΤΗΝ ΕΝΝΟΙΑ ΤΩΝ ΔΙΑΦΟΡΙΣΙΜΩΝΑ- ΠΟΛΛΑΠΛΟΤΗΤΩΝ, ΔΗΛΑΔΗ ΤΩΝ ΔΙΑΦΟΡΙΣΙΜΩΝ ΠΟΛΛΑΠΛΟΤΗΤΩΝ ΜΕ ΜΟΝΤΕΛΑ ΤΟΠΟΛΟΓΙΚΑ(ΠΕΠΕΡΑΣΜΕΝΩΣ ΠΑΡΑΓΟΜΕΝΑ ΚΑΙ ΠΡΟΒΟΛΙΚΑ) Α-ΠΡΟΤΥΠΑ. ΕΠΙΣΗΣ ΕΞΕΤΑΖΟΥΜΕ ΒΑΣΙΚΕΣ ΙΔΙΟΤΗΤΕΣ ΤΩΝ ΑΝΤΙΣΤΟΙΧΩΝ ΕΦΑΠΤΟΜΕΝΩΝ ΧΩΡΩΝ ΠΑΡΑΓΩΓΙΣΕΩΝ ΚΑΙ ΔΙΑΝΥΣΜΑΤΙΚΩΝ ΠΕΔΙΩΝ. ΤΕΛΟΣ ΜΕΛΕΤΑΜΕ ΤΙΣ ΔΙΑΦΟΡΙΣΙΜΕΣ ΔΕΣΜΕΣ ΜΕ ΝΗΜΑΤΑ ΤΟΠΟΛΟΓΙΚΑ Α-ΠΡΟΤΥΠΑ ΚΑΙΑΠΟΔΕΙΚΝΥΟΥΜΕ ΟΤΙ ΟΙ ΠΑΡΑΠΑΝΩ ΔΕΣΜΕΣ ΕΦΟΔΙΑΖΟΝΤΑΙ ΜΕ ΔΙΑΦΟΡΙΣΙΜΗ Α-ΕΡΜΙΤΙΑΝΗ ΔΟΜΗ ΚΑΙ ΣΥΜΒΙΒΑΣΤΗ ΣΥΝΟΧΗ."],"dc:identifier":["10.12681/eadd/0132","http://hdl.handle.net/10442/hedi/0132"],"dc:language":["gre"],"dc:publisher":["National and Kapodistrian University of Athens","Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)"],"dc:subject":["ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ/ΟΛΙΚΗ ΑΝΑΛΥΣΗ","ΔΙΑΦΟΡΙΣΙΜΕΣ /Α-ΔΕΣΜΕΣ","ΔΙΑΦΟΡΙΣΙΜΕΣ /Α-ΠΟΛΛΑΠΛΟΤΗΤΕΣ","Μαθηματικά","ΤΟΠΟΛΟΓΙΚΗ ΑΛΓΕΒΡΑ","DEFFERENTIABLE /A-MANIFOLDS","TOPOLOGICAL ALGEBRA","Φυσικές Επιστήμες","Natural Sciences","Mathematics"],"dc:title":["ΕΡΜΙΤΙΑΝΗ ΔΙΑΦΟΡΙΚΗ ΓΕΩΜΕΤΡΙΑ ΣΕ /Α-ΔΕΣΜΕΣ","HERMITIAN DIFFERENTIAL GEOMETRY ON /A-BUNDLES"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:24:52Z"}