Tensor calculus. Differentiable manifolds, tangent bundles. Maps of manifolds, diffeomorphism, Lie derivative. Exterior calculus. Riemann and pseudo-Riemann geometry. Covariant derivative, parallel transfer, geodesics. Torsion and curvature, space of connections. Metric derivatives, Levi-Civita derivative. Relation of Lie, exterior, and covariant derivatives. Submanifolds, integrability, Frobenius theorem. Integration on manifolds, integrable densities, integral theorems.
The lectures are aimed at students interested in theoretical physics at the end of their bachelor's or the beginning of their master's study.
This course is usually followed by the course NTMF060 – Geometrical Methods of Theoretical Physics II. However, this academic year, this course is not opened.
Lectures and practicals are scheduled each Tuesday at 14:50–18:00 in lecture room T1.
Both lectures and practicals are taught in person.
Recordings of lectures (from this and previous years) are available on a special page, the address of which was sent to enrolled students.
If anyone is interested in watching recordings of the lectures without enrolment, please, contact the lecturer by email.
This year, the lectures are given in Czech. However, the recordings of lectures in English are also available.
The examination can be both in Czech or English.
Zkouška se koná v následujících termínech:
Další termíny po domluvě s prof. Bičákem nebo prof. Krtoušem.
Zkouška se skládá z písemné (na základě odevzdaných domácích úkolů) a ústní části (2 otázky z vyložené látky).
Zkouška se skládá z písemné (výpočet křivosti metriky formalismem forem) a ústní části (2 otázky z vyložené látky).
Vedle literatury uvedené níže jsou k dispozici texty speciálně k přednášce NTMF059: