Geometry of nilpotent lie groups pdf

The book consists of twenty one chapters divided into five parts. The geometry of leftinvariant structures on nilpotent lie groups. Let rn be a connected, simply connected, abelian lie group and let h. Hypoelliptic heat kernel on nilpotent lie groups malva asaad, ph. Lorentz geometry of 2step nilpotent lie groups springerlink. Discrete uniform subgroups of solvable lie groups, trans. Lie groups as riemannian homogeneous ksymmetric spaces. Leftinvariant fstructures on 2step nilpotent and filiform lie groups. We study the geometry of a filiform nilpotent lie group endowed with a leftinvariant metric. The classification of left invariant metrics of neutral signature on the 4dimensional nilpotent lie groups is presented. The geometry of leftinvariant structures on nilpotent lie groups vitaly v. Precisely, we prove that there do not exist quasiisometric embeddings of such a nilpotent lie group into either a cat0 metric space or an alexandrov metric space with curvature bounded below.

After integrating explicitly the geodesic equations, we discuss. Lorentz geometry of 4dimensional nilpotent lie groups. We investigate their geometry, especially holonomy groups and decomposability of these metrics. It is known that if n is a simply connected nilpotent lie group with lie algebra, then exp. N is a diffeomorphism, where exp denotes the lie group exponential map.

Pdf geometry of central extensions of nilpotent lie algebras. Precisely, we prove that there do not exist quasiisometric embeddings of such a nilpotent lie group into either a cat0 metric space or an alexandrov metric space. Balashchenko belarusian state university, minsk, belarus xix geometrical seminar zlatibor, serbia, august 28 september 4, 2016 main goals. The geometry of leftinvariant structures on nilpotent lie.

Geometry of 2step nilpotent groups with a left invariant. The large scale geometry of nilpotent lie groups 953 metric spaces which are locally cat k or cbb k. Subriemannian structures on nilpotent lie groups rory biggs geometry, graphs and control ggc research group department of mathematics, rhodes university, grahamstown, south africa. I am trying to understand the noncommutative analysis for nilpotent lie groups, so ive been reading corwins and greenleafs book on the representation theory of nilpotent groups and going through. Let n be the unique, simply connected, 2step nilpotent lie group whose lie algebra is at, and equip n with the left invariant metric determined by the inner. Ruth gornet, the length spectrum and representation theory on two and threestep nilpotent lie groups, in geometry of the spectrum %seattle, wa, 1993, %volume 173 of contemp. University of connecticut, 2016 abstract the starting point of our analysis is an old idea of writing an eigenfunction expan.