The Geometry of Filiform Nilpotent Lie Groups
نویسندگان
چکیده
We study the geometry of a filiform nilpotent Lie group endowed with a leftinvariant metric. We describe the connection and curvatures, and we investigate necessary and sufficient conditions for subgroups to be totally geodesic submanifolds. We also classify the one-parameter subgroups which are geodesics. Department of Mathematics, Wellesley College, 106 Central St., Wellesley, MA 02481-8203 [email protected] Department of Mathematics, Idaho State University, Pocatello, ID 83209-8085 [email protected], [email protected]
منابع مشابه
Solvable Lie algebras with $N(R_n,m,r)$ nilradical
In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.
متن کاملEla Solvable 3 - Lie Algebras with a Maximal Hypo - Nilpotent Ideal N ∗
Abstract. This paper obtains all solvable 3-Lie algebras with the m-dimensional filiform 3-Lie algebra N (m ≥ 5) as a maximal hypo-nilpotent ideal, and proves that the m-dimensional filiform 3-Lie algebra N can’t be as the nilradical of solvable non-nilpotent 3-Lie algebras. By means of one dimensional extension of Lie algebras to the 3-Lie algebras, we get some classes of solvable Lie algebras...
متن کاملSymbolic and Iterative Computation of Quasi-Filiform Nilpotent Lie Algebras of Dimension Nine
This paper addresses the problem of computing the family of two-filiform Lie algebra laws of dimension nine using three Lie algebra properties converted into matrix form properties: Jacobi identity, nilpotence and quasi-filiform property. The interest in this family is broad, both within the academic community and the industrial engineering community, since nilpotent Lie algebras are applied in...
متن کاملLie Algebra Prederivations and Strongly Nilpotent Lie Algebras
We study Lie algebra prederivations. A Lie algebra admitting a non-singular prederivation is nilpotent. We classify filiform Lie algebras admitting a non-singular prederivation but no non-singular derivation. We prove that any 4-step nilpotent Lie algebra admits a non-singular prederivation.
متن کاملsolvmanifolds with a simple Einstein derivation
The structure of a solvable Lie groups admitting an Einstein left-invariant metric is, in a sense, completely determined by the nilradical of its Lie algebra. We give an easy-to-check necessary and sufficient condition for a nilpotent algebra to be an Einstein nilradical whose Einstein derivation has simple eigenvalues. As an application, we classify filiform Einstein nilradicals (modulo known ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008