FAZIL, A. Geodetické křivky v sub-Riemannovské geometrii [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2025.

Posudek vedoucího

Návrat, Aleš

The student's thesis deals with geodesic curves in sub-Riemannian geometry, which is a rather difficult topic requiring a solid knowledge of the fundamentals of differential geometry. In addition, the student started very slowly, and it seemed that there was no chance of completing this work. Fortunately, he is a really good student, so in the end he managed everything and delivered quite a nice piece of work. However, in the introductory theoretical part and the example part, the haste is still visible, and some parts are not well formulated at all. However, I see the main shortcomings in the unfinished Chapter 7 and especially in the examples, where the derived theory should have been better demonstrated. Examples 8.3 and 8.4 are unfinished, they lack testing of the singular solution on Hamilton's equations. Considering the difficulty of the work, I rate it with a C.

Posudek oponenta

Hrdina, Jaroslav

Chapters 1-4 introduce the basics of differential geometry, These chapters are written in standard quality. They do not contain any mathematical errors, but some of the concepts they use are not predefined (for example, sub-manifold). In several places, italics are used instead of bold type to define a term (pg. 15). Overall, I would expect numbered displays and references to them in the text (they are only in chapters 6 and 8, which seems inconsistent ) In Theorem 5.6. General description of the theorem  "A classical.." does not belong in the theorem itself. Chapter 2.3, the correct term is a smooth section, not portions. Page 22, the first sentence ends strangely. page 26, Lagrangian L was on the previous page F^* Corollary 2.6 is the corollary of which theorem? The dot is defined as a derivative according to s (normally it is according to t) without comment.  ------------------------------------------------------------- Chapters 4-7 contain the basics of control theory, more advanced mathematics, and examples. They are of average quality.  Again, they do not contain any mathematical errors. The proofs are insufficiently commented on, which makes it difficult to understand. The proof on page 27 is unnecessarily drawn out. The Heisenberg Case is being resolved in stages, and there is no comment referring to the previous parts.  -------------------------------- Chapter 8 contains mainly examples.  Language and editing style have become significantly worse, with more typos (e.g., first page: horizontal -> horizontal, one-connection form -> connection one form, `... ). Something is wrong with citations "[?]"! The First g_{ij} is Riemannian (non sub Riemannian) The descriptions of the example calculations are not properly commented on and are very difficult to read.  ---------------------------------------- The reference [2] is not cited in the text ------------------------------------------ Overall, this is a very interesting topic. I enjoy that the work is based on examples that demonstrate various situations. It is unfortunate that the text is not well-written, especially in the example part. 

eVSKP id 166387