{"id":{"repo_id":"cagliari","oai_identifier":"oai:iris.unica.it:11584/266004"},"canonical_url":"https://search.dev.ndltd.org/etd/cagliari/oai:iris.unica.it:11584/266004","repository":{"repo_id":"cagliari","name":"Università di Cagliari","base_url":"https://iris.unica.it/oai/request"},"display":{"title":"Sugli spazi omogenei di dimensione tre SO(2) - isotropi","abstract":"In this thesis we studied some problems from the theory of the submanifolds of the three-dimensional Riemannian manifolds. Our intention is to evaluate which properties of the submanifolds depend by the dimension of the group of isometries. We considered a two-parameter family of three-dimensional Riemannian manifolds (M, ds2 l,m), endowed with the Cartan - Vranceanu metrics. These metrics can be found in the classification of 3-dimensional homogeneous metrics given by L. Bianchi. Their geometric interest lies in the following fact: the family of metrics includes all 3-dimensional homogeneous metrics whose group of isometries has dimension 4 or 6, except for those of constant negative sectional curvature. The group of isometries of these spaces has a subgroup isomorphic to the group SO(2), so there exist surfaces of revolution around z-axis. We explicitly obtained the Lie algebra of the Killing vector fields and thus the group of isometries for the C-V metrics. We determined the equations of the geodesics using the Killing vector fields and obtain explicitly the equation of the surface which con- tains the geodesics. After having determined the totally geodesics surfaces isometrically immersed in the C-V spaces, we studied the totally umbili- cal submanifolds of these spaces, proving that the only totally umbilical submanifolds are totally geodesic. We found the geodesics for the SO(2)- invariant surfaces of the Cartan-Vranceanu spaces, deduced the conditions that meridians and parallels must satisfy in order to be geodesics and show the analogies with the euclidian case.","abstract_html":"In this thesis we studied some problems from the theory of the submanifolds of the three-dimensional Riemannian manifolds. Our intention is to evaluate which properties of the submanifolds depend by the dimension of the group of isometries. We considered a two-parameter family of three-dimensional Riemannian manifolds (M, ds2 l,m), endowed with the Cartan - Vranceanu metrics. These metrics can be found in the classification of 3-dimensional homogeneous metrics given by L. Bianchi. Their geometric interest lies in the following fact: the family of metrics includes all 3-dimensional homogeneous metrics whose group of isometries has dimension 4 or 6, except for those of constant negative sectional curvature. The group of isometries of these spaces has a subgroup isomorphic to the group SO(2), so there exist surfaces of revolution around z-axis. We explicitly obtained the Lie algebra of the Killing vector fields and thus the group of isometries for the C-V metrics. We determined the equations of the geodesics using the Killing vector fields and obtain explicitly the equation of the surface which con- tains the geodesics. After having determined the totally geodesics surfaces isometrically immersed in the C-V spaces, we studied the totally umbili- cal submanifolds of these spaces, proving that the only totally umbilical submanifolds are totally geodesic. We found the geodesics for the SO(2)- invariant surfaces of the Cartan-Vranceanu spaces, deduced the conditions that meridians and parallels must satisfy in order to be geodesics and show the analogies with the euclidian case.","abstract_has_math":false,"creators":["PROFIR, MARIA MANUELA"],"institution":"Università degli Studi di Cagliari","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2008,"date_issued":"2008-10","date_published":"2008-10","updated_at":"2026-07-24T01:30:05Z","subjects":["Cartan - Vranceanu metrics","Geodesics","Geodesics of rotational surfaces","Group of isometries","Killing vectors Fields","Settore MAT/03 - Geometria"],"languages":["ita"],"rights":["info:eu-repo/semantics/closedAccess","license:Non specificato"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11584/266004","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["PROFIR, MARIA MANUELA"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2008-10"]},{"key":"dc:publisher","label":"Institution","values":["Università degli Studi di Cagliari"]},{"key":"dc:relation","label":"Dc Relation","values":["numberofpages:123"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Cartan - Vranceanu metrics","Geodesics","Geodesics of rotational surfaces","Group of isometries","Killing vectors Fields","Settore MAT/03 - Geometria"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["ita"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/closedAccess","license:Non specificato"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/11584/266004"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we studied some problems from the theory of the submanifolds of the three-dimensional Riemannian manifolds. Our intention is to evaluate which properties of the submanifolds depend by the dimension of the group of isometries. We considered a two-parameter family of three-dimensional Riemannian manifolds (M, ds2 l,m), endowed with the Cartan - Vranceanu metrics. These metrics can be found in the classification of 3-dimensional homogeneous metrics given by L. Bianchi. Their geometric interest lies in the following fact: the family of metrics includes all 3-dimensional homogeneous metrics whose group of isometries has dimension 4 or 6, except for those of constant negative sectional curvature. The group of isometries of these spaces has a subgroup isomorphic to the group SO(2), so there exist surfaces of revolution around z-axis. We explicitly obtained the Lie algebra of the Killing vector fields and thus the group of isometries for the C-V metrics. We determined the equations of the geodesics using the Killing vector fields and obtain explicitly the equation of the surface which con- tains the geodesics. After having determined the totally geodesics surfaces isometrically immersed in the C-V spaces, we studied the totally umbili- cal submanifolds of these spaces, proving that the only totally umbilical submanifolds are totally geodesic. We found the geodesics for the SO(2)- invariant surfaces of the Cartan-Vranceanu spaces, deduced the conditions that meridians and parallels must satisfy in order to be geodesics and show the analogies with the euclidian case."]},{"key":"dc:title","label":"Title","values":["Sugli spazi omogenei di dimensione tre SO(2) - isotropi"]}]}],"canonical_facts":{"dc:creator":["PROFIR, MARIA MANUELA"],"dc:date":["2008-10"],"dc:description":["In this thesis we studied some problems from the theory of the submanifolds of the three-dimensional Riemannian manifolds. Our intention is to evaluate which properties of the submanifolds depend by the dimension of the group of isometries. We considered a two-parameter family of three-dimensional Riemannian manifolds (M, ds2 l,m), endowed with the Cartan - Vranceanu metrics. These metrics can be found in the classification of 3-dimensional homogeneous metrics given by L. Bianchi. Their geometric interest lies in the following fact: the family of metrics includes all 3-dimensional homogeneous metrics whose group of isometries has dimension 4 or 6, except for those of constant negative sectional curvature. The group of isometries of these spaces has a subgroup isomorphic to the group SO(2), so there exist surfaces of revolution around z-axis. We explicitly obtained the Lie algebra of the Killing vector fields and thus the group of isometries for the C-V metrics. We determined the equations of the geodesics using the Killing vector fields and obtain explicitly the equation of the surface which con- tains the geodesics. After having determined the totally geodesics surfaces isometrically immersed in the C-V spaces, we studied the totally umbili- cal submanifolds of these spaces, proving that the only totally umbilical submanifolds are totally geodesic. We found the geodesics for the SO(2)- invariant surfaces of the Cartan-Vranceanu spaces, deduced the conditions that meridians and parallels must satisfy in order to be geodesics and show the analogies with the euclidian case."],"dc:identifier":["http://hdl.handle.net/11584/266004"],"dc:language":["ita"],"dc:publisher":["Università degli Studi di Cagliari"],"dc:relation":["numberofpages:123"],"dc:rights":["info:eu-repo/semantics/closedAccess","license:Non specificato"],"dc:subject":["Cartan - Vranceanu metrics","Geodesics","Geodesics of rotational surfaces","Group of isometries","Killing vectors Fields","Settore MAT/03 - Geometria"],"dc:title":["Sugli spazi omogenei di dimensione tre SO(2) - isotropi"],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-24T01:30:05Z"}