MU03048 Differential Invariants

Mathematical Institute in Opava
Winter 2019
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Students obtain basic knowledge of differential invariants and their applications. Differential invariants are a tool to solve the problem of equivalence of geometric structures with respect to a class of transformations.
Syllabus
  • Jet bundles
    Lie transformations
    Lie vector fields
    Lie pseudogroups
    Differential invariants
    Classification of linear ODEs up to equivalence
    Differential invariants in natural bundles
    G-structures
Literature
    recommended literature
  • V. Yumaguzhin. Introduction to Differential Invariants. 2005. URL info
  • P. J. Olver. Equivalence, Invariants, and Symmetry. Cambridge University Press, Cambridge, 1995. ISBN 0-521-47811-1. info
  • S. Sternberg. Lectures on Differential Geometry. AMS Chelsea Publishing, Providence, Rhode Island, 1982. info
  • S. Kobayashi. Transformation groups in differential geometry. Springer-Verlag, Berlin - Heidelberg - New York, 1972. info
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
Teacher's information
Oral examination.
The course is also listed under the following terms Winter 1998, Summer 1999, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018.
  • Enrolment Statistics (recent)
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