{"id":{"repo_id":"greece","oai_identifier":"oai:10442/0188"},"canonical_url":"https://search.dev.ndltd.org/etd/greece/oai:10442/0188","repository":{"repo_id":"greece","name":"Greek National Archive of PhD Theses","base_url":"https://phdtheses.ekt.gr/eadd_oai/request"},"display":{"title":"ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN ΥΠΕΡΒΟΛΙΚΟΥ ΤΥΠΟΥ","abstract":"THE AIM OF THE PRESENT THESIS IS TO EXAMINE THE CLOSED GEODESICS ON COMPACT RIEMANNIAN MANIFOLDS OF HYPERBOLIC TYPE; THAT MEANS RIEMANNIAN MANIFOLDS WHICH CAN CARRY A RIEMANNIAN METRIC WITH STRICTLY NEGATIVE SECTIONAL CURVATURE. IT ISPROVED, THAT THE INDEX OF THE M- COVER OF ONE CLOSED GEODESIC ON A COMPACT RIEMANNIAN, MANIFOLD WITHOUT CONJUGATE POINTS IS ZERO, THAT MEANS INDEX ΛΜ CM = 0. IT IS ALSO PROVED, THAT THE SET OF CLOSED GEODESICS, ON A COMPACT RIEMANNIANMANIFOLD OF HYPERBOLIC TYPE, WITHOUT CONJUGATE POINTS STILL AT INFINITY, IS DENSE IN THE SET OF ALL CLOSED DIFFERENTIABLE CURVES ON THE MANIFOLD.","abstract_html":"THE AIM OF THE PRESENT THESIS IS TO EXAMINE THE CLOSED GEODESICS ON COMPACT RIEMANNIAN MANIFOLDS OF HYPERBOLIC TYPE; THAT MEANS RIEMANNIAN MANIFOLDS WHICH CAN CARRY A RIEMANNIAN METRIC WITH STRICTLY NEGATIVE SECTIONAL CURVATURE. IT ISPROVED, THAT THE INDEX OF THE M- COVER OF ONE CLOSED GEODESIC ON A COMPACT RIEMANNIAN, MANIFOLD WITHOUT CONJUGATE POINTS IS ZERO, THAT MEANS INDEX ΛΜ CM = 0. IT IS ALSO PROVED, THAT THE SET OF CLOSED GEODESICS, ON A COMPACT RIEMANNIANMANIFOLD OF HYPERBOLIC TYPE, WITHOUT CONJUGATE POINTS STILL AT INFINITY, IS DENSE IN THE SET OF ALL CLOSED DIFFERENTIABLE CURVES ON THE MANIFOLD.","abstract_has_math":false,"creators":["Χριστοφορίδου, Χρυσή"],"institution":"Aristotle University Of Thessaloniki (AUTH)","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":"2026-07-24T02:25:08Z","subjects":["CONJUGATE POINTS","DIFFERENTIABLE CURVES","Geodesic curves","HILBERT MANIFOLDS","HYPERBOLIC MANIFOLDS","JACOBI VECTOR FIELDS","M-COVER INDEX","MONIFOLDS OF HYPERBOLIC TYPE","Riemannian manifolds","SECTIONAL CURVATURE","Γεωδαισιακές καμπύλες","ΔΕΙΚΤΗΣ Μ-ΚΑΛΥΜΜΑΤΟΣ","ΔΙΑΝΥΣΜΑΤΙΚΑ ΠΕΔΙΑ ΤΟΥ JACOBI","Διαφορική γεωμετρία","ΔΙΑΦΟΡΙΣΙΜΕΣ ΚΑΜΠΥΛΕΣ","ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ HILBERT","Πολλαπλότητες του Riemann","ΣΥΖΥΓΗ ΣΗΜΕΙΑ","ΤΜΗΜΑΤΙΚΗ ΚΑΜΠΥΛΟΤΗΤΑ","ΥΠΕΡΒΟΛΙΚΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"languages":["gre"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["10.12681/eadd/0188"],"render_values":[{"text":"10.12681/eadd/0188","href":"https://doi.org/10.12681/eadd/0188","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10442/hedi/0188","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Χριστοφορίδου, Χρυσή"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["1986"]},{"key":"dc:publisher","label":"Institution","values":["Aristotle University Of Thessaloniki (AUTH)","Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)"]},{"key":"dc:type","label":"Dc Type","values":["PhD Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["CONJUGATE POINTS","DIFFERENTIABLE CURVES","Geodesic curves","HILBERT MANIFOLDS","HYPERBOLIC MANIFOLDS","JACOBI VECTOR FIELDS","M-COVER INDEX","MONIFOLDS OF HYPERBOLIC TYPE","Riemannian manifolds","SECTIONAL CURVATURE","Γεωδαισιακές καμπύλες","ΔΕΙΚΤΗΣ Μ-ΚΑΛΥΜΜΑΤΟΣ","ΔΙΑΝΥΣΜΑΤΙΚΑ ΠΕΔΙΑ ΤΟΥ JACOBI","Διαφορική γεωμετρία","ΔΙΑΦΟΡΙΣΙΜΕΣ ΚΑΜΠΥΛΕΣ","ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ HILBERT","Πολλαπλότητες του Riemann","ΣΥΖΥΓΗ ΣΗΜΕΙΑ","ΤΜΗΜΑΤΙΚΗ ΚΑΜΠΥΛΟΤΗΤΑ","ΥΠΕΡΒΟΛΙΚΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ","Φυσικές Επιστήμες","Μαθηματικά","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/0188","http://hdl.handle.net/10442/hedi/0188"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["THE AIM OF THE PRESENT THESIS IS TO EXAMINE THE CLOSED GEODESICS ON COMPACT RIEMANNIAN MANIFOLDS OF HYPERBOLIC TYPE; THAT MEANS RIEMANNIAN MANIFOLDS WHICH CAN CARRY A RIEMANNIAN METRIC WITH STRICTLY NEGATIVE SECTIONAL CURVATURE. IT ISPROVED, THAT THE INDEX OF THE M- COVER OF ONE CLOSED GEODESIC ON A COMPACT RIEMANNIAN, MANIFOLD WITHOUT CONJUGATE POINTS IS ZERO, THAT MEANS INDEX ΛΜ CM = 0. IT IS ALSO PROVED, THAT THE SET OF CLOSED GEODESICS, ON A COMPACT RIEMANNIANMANIFOLD OF HYPERBOLIC TYPE, WITHOUT CONJUGATE POINTS STILL AT INFINITY, IS DENSE IN THE SET OF ALL CLOSED DIFFERENTIABLE CURVES ON THE MANIFOLD.","ΑΝΤΙΚΕΙΜΕΝΟ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΑΥΤΗΣ ΕΙΝΑΙ Η ΜΕΛΕΤΗ ΤΩΝ ΚΛΕΙΣΤΩΝ ΓΕΩΔΑΙΣΙΑΚΩΝ ΚΑΜΠΥΛΩΝ ΣΕ ΣΥΜΠΑΓΕΙΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN (M, G) ΥΠΕΡΒΟΛΙΚΟΥ ΤΥΠΟΥ, ΔΗΛΑΔΗ ΣΥΜΠΑΓΕΙΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN ΟΙ ΟΠΟΙΕΣ ΜΠΟΡΟΥΝ ΝΑ ΕΦΟΔΙΑΣΤΟΥΝ ΜΕ ΜΙΑ ΜΕΤΡΙΚΗ ΤΟΥ RIEMANN G*, ΩΣ ΠΡΟΣ ΤΗΝ ΟΠΟΙΑ Η ΤΜΗΜΑΤΙΚΗ ΚΑΜΠΥΛΟΤΗΤΑ Κ* ΕΙΝΑΙ ΑΥΣΤΗΡΩΣ ΑΡΝΗΤΙΚΗ. ΣΤΗΝ ΑΡΧΗ ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΟΤΙ Ο ΔΕΙΚΤΗΣ ΤΟΥ M-ΚΑΛΥΜΜΑΤΟΣ ΜΙΑΣ ΚΛΕΙΣΤΗΣ ΓΕΩΔΙΑΣΙΑΚΗΣ ΚΑΜΠΥΛΗΣ C, ΣΕ ΜΙΑ ΣΥΜΠΑΓΗ ΠΟΛΛΑΠΛΟΤΗΤΑ ΤΟΥ RIEMANN ΧΩΡΙΣ ΣΥΖΥΓΗ ΣΗΜΕΙΑ, ΕΙΝΑΙ ΜΗΔΕΝ, ΔΗΛΑΔΗ INDEX ΛΜ CM = 0. ΣΤΗ ΣΥΝΕΧΕΙΑ ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΟΤΙ ΣΕ ΣΥΜΠΑΓΕΙΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN (M, G) ΥΠΕΡΒΟΛΙΚΟΥ ΤΥΠΟΥ ΧΩΡΙΣ ΣΥΖΥΓΗ ΣΗΜΕΙΑ ΑΚΟΜΗ ΚΑΙ ΣΤΟ ΑΠΕΙΡΟ, ΟΙ ΚΛΕΙΣΤΕΣ ΓΕΩΔΑΙΣΙΑΚΕΣ ΚΑΜΠΥΛΕΣ ΑΠΟΤΕΛΟΥΝ ΣΥΝΟΛΟ ΠΥΚΝΟ ΣΤΟ ΣΥΝΟΛΟ ΤΩΝ ΔΙΑΦΟΡΙΣΙΜΩΝ ΚΑΜΠΥΛΩΝ ΤΗΣ ΠΟΛΛΑΠΛΟΤΗΤΑΣ Μ."]},{"key":"dc:title","label":"Title","values":["ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN ΥΠΕΡΒΟΛΙΚΟΥ ΤΥΠΟΥ","RIEMANNIAN MANIFOLDS OF HYPERBOLIC TYPE"]}]}],"canonical_facts":{"dc:creator":["Χριστοφορίδου, Χρυσή"],"dc:date":["1986"],"dc:description":["THE AIM OF THE PRESENT THESIS IS TO EXAMINE THE CLOSED GEODESICS ON COMPACT RIEMANNIAN MANIFOLDS OF HYPERBOLIC TYPE; THAT MEANS RIEMANNIAN MANIFOLDS WHICH CAN CARRY A RIEMANNIAN METRIC WITH STRICTLY NEGATIVE SECTIONAL CURVATURE. IT ISPROVED, THAT THE INDEX OF THE M- COVER OF ONE CLOSED GEODESIC ON A COMPACT RIEMANNIAN, MANIFOLD WITHOUT CONJUGATE POINTS IS ZERO, THAT MEANS INDEX ΛΜ CM = 0. IT IS ALSO PROVED, THAT THE SET OF CLOSED GEODESICS, ON A COMPACT RIEMANNIANMANIFOLD OF HYPERBOLIC TYPE, WITHOUT CONJUGATE POINTS STILL AT INFINITY, IS DENSE IN THE SET OF ALL CLOSED DIFFERENTIABLE CURVES ON THE MANIFOLD.","ΑΝΤΙΚΕΙΜΕΝΟ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΑΥΤΗΣ ΕΙΝΑΙ Η ΜΕΛΕΤΗ ΤΩΝ ΚΛΕΙΣΤΩΝ ΓΕΩΔΑΙΣΙΑΚΩΝ ΚΑΜΠΥΛΩΝ ΣΕ ΣΥΜΠΑΓΕΙΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN (M, G) ΥΠΕΡΒΟΛΙΚΟΥ ΤΥΠΟΥ, ΔΗΛΑΔΗ ΣΥΜΠΑΓΕΙΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN ΟΙ ΟΠΟΙΕΣ ΜΠΟΡΟΥΝ ΝΑ ΕΦΟΔΙΑΣΤΟΥΝ ΜΕ ΜΙΑ ΜΕΤΡΙΚΗ ΤΟΥ RIEMANN G*, ΩΣ ΠΡΟΣ ΤΗΝ ΟΠΟΙΑ Η ΤΜΗΜΑΤΙΚΗ ΚΑΜΠΥΛΟΤΗΤΑ Κ* ΕΙΝΑΙ ΑΥΣΤΗΡΩΣ ΑΡΝΗΤΙΚΗ. ΣΤΗΝ ΑΡΧΗ ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΟΤΙ Ο ΔΕΙΚΤΗΣ ΤΟΥ M-ΚΑΛΥΜΜΑΤΟΣ ΜΙΑΣ ΚΛΕΙΣΤΗΣ ΓΕΩΔΙΑΣΙΑΚΗΣ ΚΑΜΠΥΛΗΣ C, ΣΕ ΜΙΑ ΣΥΜΠΑΓΗ ΠΟΛΛΑΠΛΟΤΗΤΑ ΤΟΥ RIEMANN ΧΩΡΙΣ ΣΥΖΥΓΗ ΣΗΜΕΙΑ, ΕΙΝΑΙ ΜΗΔΕΝ, ΔΗΛΑΔΗ INDEX ΛΜ CM = 0. ΣΤΗ ΣΥΝΕΧΕΙΑ ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΟΤΙ ΣΕ ΣΥΜΠΑΓΕΙΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN (M, G) ΥΠΕΡΒΟΛΙΚΟΥ ΤΥΠΟΥ ΧΩΡΙΣ ΣΥΖΥΓΗ ΣΗΜΕΙΑ ΑΚΟΜΗ ΚΑΙ ΣΤΟ ΑΠΕΙΡΟ, ΟΙ ΚΛΕΙΣΤΕΣ ΓΕΩΔΑΙΣΙΑΚΕΣ ΚΑΜΠΥΛΕΣ ΑΠΟΤΕΛΟΥΝ ΣΥΝΟΛΟ ΠΥΚΝΟ ΣΤΟ ΣΥΝΟΛΟ ΤΩΝ ΔΙΑΦΟΡΙΣΙΜΩΝ ΚΑΜΠΥΛΩΝ ΤΗΣ ΠΟΛΛΑΠΛΟΤΗΤΑΣ Μ."],"dc:identifier":["10.12681/eadd/0188","http://hdl.handle.net/10442/hedi/0188"],"dc:language":["gre"],"dc:publisher":["Aristotle University Of Thessaloniki (AUTH)","Αριστοτέλειο Πανεπιστήμιο Θεσσαλονίκης (ΑΠΘ)"],"dc:subject":["CONJUGATE POINTS","DIFFERENTIABLE CURVES","Geodesic curves","HILBERT MANIFOLDS","HYPERBOLIC MANIFOLDS","JACOBI VECTOR FIELDS","M-COVER INDEX","MONIFOLDS OF HYPERBOLIC TYPE","Riemannian manifolds","SECTIONAL CURVATURE","Γεωδαισιακές καμπύλες","ΔΕΙΚΤΗΣ Μ-ΚΑΛΥΜΜΑΤΟΣ","ΔΙΑΝΥΣΜΑΤΙΚΑ ΠΕΔΙΑ ΤΟΥ JACOBI","Διαφορική γεωμετρία","ΔΙΑΦΟΡΙΣΙΜΕΣ ΚΑΜΠΥΛΕΣ","ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ HILBERT","Πολλαπλότητες του Riemann","ΣΥΖΥΓΗ ΣΗΜΕΙΑ","ΤΜΗΜΑΤΙΚΗ ΚΑΜΠΥΛΟΤΗΤΑ","ΥΠΕΡΒΟΛΙΚΕΣ ΠΟΛΛΑΠΛΟΤΗΤΕΣ","Φυσικές Επιστήμες","Μαθηματικά","Natural Sciences","Mathematics"],"dc:title":["ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN ΥΠΕΡΒΟΛΙΚΟΥ ΤΥΠΟΥ","RIEMANNIAN MANIFOLDS OF HYPERBOLIC TYPE"],"dc:type":["PhD Thesis"]},"updated_at":"2026-07-24T02:25:08Z"}