Riemannian algebras of lie groups = 리 군의 리만 대수

Because many notions of differential geometry is defined by the use of connections on differential manifolds, the study of connections on differential manifolds is important in differential geometry. Many mathematician research the invariant connections on Lie groups and homogeneous spaces by using algebraic language since Lie groups and homogeneous space have relations with Lie algebras. In this thesis, we classify the Riemannian invariant connections of Lie groups by determining the Riemannian algebras. First, we see that Riemannian invariant connections is represented in terms of Riemannian algebras and review the relation between psuedo-Riemannian algebras of Lie groups and symmetric Lie algebras. We classify the symmetric Lie algebras of dimension 4, 5 and determine Riemannian invariant connections of Lie group of dimension 2, 3 by classifying Riemannian algebras of 2, 3-dimensional Lie group. In case of dimension 3, we determine Riemannian algebras by treating the unimodular and nonunimodular cases separately and show the relation between Riemanian algebras of unimodular Lie groups and Jacobi elliptic algebras. Finally, we classify Riemannian algebras of Heisenberg group.
Advisors
Myung, Hyo-Chulresearcher명효철researcher
Publisher
한국과학기술원
Issue Date
2002
Identifier
177219/325007 / 000965820
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학전공, 2002.8, [ [ii], 72, [1] p. ]

Keywords

리 대수; 아핀 접속; 리 군; 리만 대수; Lie algebra; Lie group; affine connection; Riemannian algebra

URI
http://hdl.handle.net/10203/41850
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=177219&flag=t
Appears in Collection
MA-Theses_Ph.D.(박사논문)
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