Geodetické křivky v sub-Riemannovské geometrii
| but.committee | doc. Ing. Luděk Nechvátal, Ph.D. (předseda) prof. RNDr. Josef Šlapal, CSc. (místopředseda) doc. Ing. Petr Tomášek, Ph.D. (člen) doc. Ing. Jiří Šremr, Ph.D. (člen) prof. RNDr. Miloslav Druckmüller, CSc. (člen) Prof. Bruno Rubino, Ph.D. (člen) Assoc. Prof. Matteo Colangeli, PhD. (člen) | cs |
| but.defence | The student presented their Master's thesis to the examination committee. The secretary of the committee read aloud the evaluation reports of both the thesis supervisor and the opponent. Following this, the examination proceeded with the opponent’s questions. The student responded to these questions appropriately. prof. RNDr. Josef Šlapal, CSc. asked the student to define the concept of a manifold. The student handled the question sufficiently. | cs |
| but.jazyk | angličtina (English) | |
| but.program | Applied and Interdisciplinary Mathematics | cs |
| but.result | práce byla úspěšně obhájena | cs |
| dc.contributor.advisor | Návrat, Aleš | en |
| dc.contributor.author | Fazil, Adnan | en |
| dc.contributor.referee | Hrdina, Jaroslav | en |
| dc.date.created | 2025 | cs |
| dc.description.abstract | This thesis investigates the fundamental ideas and comparative structure of Riemannian and sub- Riemannian geodesics, the curves that locally minimise length. Geodesics, as defined variationally and by the Levi-Civita connection, are the shortest and straightest paths in Riemannian geometry. By limiting motion to a particular distribution within the tangent bundle, sub-Riemannian geometry expands on these ideas and creates a more complex and diverse class of geodesics, including regular and singular types. A thorough classification of normal and abnormal geodesics can beachieved by the study’s emphasis on the Lagrangian framework for obtaining geodesic equations under non-holonomic constraints. | en |
| dc.description.abstract | This thesis investigates the fundamental ideas and comparative structure of Riemannian and sub- Riemannian geodesics, the curves that locally minimise length. Geodesics, as defined variationally and by the Levi-Civita connection, are the shortest and straightest paths in Riemannian geometry. By limiting motion to a particular distribution within the tangent bundle, sub-Riemannian geometry expands on these ideas and creates a more complex and diverse class of geodesics, including regular and singular types. A thorough classification of normal and abnormal geodesics can beachieved by the study’s emphasis on the Lagrangian framework for obtaining geodesic equations under non-holonomic constraints. | cs |
| dc.description.mark | C | cs |
| dc.identifier.citation | FAZIL, A. Geodetické křivky v sub-Riemannovské geometrii [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2025. | cs |
| dc.identifier.other | 166387 | cs |
| dc.identifier.uri | http://hdl.handle.net/11012/254242 | |
| dc.language.iso | en | cs |
| dc.publisher | Vysoké učení technické v Brně. Fakulta strojního inženýrství | cs |
| dc.rights | Standardní licenční smlouva - přístup k plnému textu bez omezení | cs |
| dc.subject | Riemannian geometry | en |
| dc.subject | sub-Riemannian geometry | en |
| dc.subject | geodesics | en |
| dc.subject | Levi-Civita connection | en |
| dc.subject | horizontal curves | en |
| dc.subject | non-holonomic constraints | en |
| dc.subject | Lagrange multipliers | en |
| dc.subject | Euler–Lagrange equations | en |
| dc.subject | abnormal geodesics. | en |
| dc.subject | Riemannian geometry | cs |
| dc.subject | sub-Riemannian geometry | cs |
| dc.subject | geodesics | cs |
| dc.subject | Levi-Civita connection | cs |
| dc.subject | horizontal curves | cs |
| dc.subject | non-holonomic constraints | cs |
| dc.subject | Lagrange multipliers | cs |
| dc.subject | Euler–Lagrange equations | cs |
| dc.subject | abnormal geodesics. | cs |
| dc.title | Geodetické křivky v sub-Riemannovské geometrii | en |
| dc.title.alternative | Geodesics in Sub-Riemannian Geometry | cs |
| dc.type | Text | cs |
| dc.type.driver | masterThesis | en |
| dc.type.evskp | diplomová práce | cs |
| dcterms.dateAccepted | 2025-06-18 | cs |
| dcterms.modified | 2025-06-20-12:24:32 | cs |
| eprints.affiliatedInstitution.faculty | Fakulta strojního inženýrství | cs |
| sync.item.dbid | 166387 | en |
| sync.item.dbtype | ZP | en |
| sync.item.insts | 2025.08.27 02:58:12 | en |
| sync.item.modts | 2025.08.26 20:01:53 | en |
| thesis.discipline | bez specializace | cs |
| thesis.grantor | Vysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematiky | cs |
| thesis.level | Inženýrský | cs |
| thesis.name | Ing. | cs |