Geometry and Topology (17/18)
Faculteit  Science and Engineering 
Jaar  2017/18 
Vakcode  WMMA13000 
Vaknaam  Geometry and Topology (17/18) 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester I a 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Geometry and Topology (tweejaarlijks 2017/2018)  
Leerdoelen  At the end of the course, the student is able to:  derive or reproduce the formula for Christoffel symbols of a LeviCivita connection associated with a Riemannian metric on a smooth manifold,  calculate lengths of trajectories or their intersection angles, areas of surfaces and volumes of threedimensional domains,  paralleltransport (co)vectors along a given curve, to find the (classes of) geodesics and outline their properties, and to distinguish between manifolds by using their invariants such as the Riemann, Ricci, or scalar curvatures. 

Omschrijving  This is an advanced course in Riemannian geometry. It is equally oriented towards mathematicians and physicists. The material of the course covers standard notions, objects, and structures such as manifolds, tensor fields, metric tensor, LeviCivita connections and Christoffel symbols, parallel transport, geodesics (as the locally shortest), and the Riemann, Ricci, and scalar curvature tensors. The notions of vector bundles beyond the tangent bundle and smooth fibre bundles will conclude the course. The lectures aim is to communicate a firm theoretical background, including a familiarity with the proofs of the structures' properties, and ability to apply the formalism in General Relativity or Field Theory. In the last weeks of the course, the students will be offered an option to report on their own courserelated background and research progress. A familiarity with basics of General Relativity would facilitate the study yet it is not a compulsory prerequisite. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(max(100% exam, 45% from homeworks + 55% exam).) 

Vaksoort  master  
Coördinator  A.V. Kiselev  
Docent(en)  A.V. Kiselev  
Verplichte literatuur 


Entreevoorwaarden  A familiarity with basics of General Relativity would facilitate the study yet it is not a compulsory prerequisite.  
Opmerkingen  This course unit prepares for Geometry and Differential Equations, General Relativity.  
Opgenomen in 
