MU03048 Differential Invariants

Mathematical Institute in Opava
Winter 2015
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 also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
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)
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 2016, Winter 2017, Winter 2018, Winter 2019.
  • Enrolment Statistics (Winter 2015, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2015/MU03048