He describes Lie groups and their representations, with a focus on the quantum mechanically relevant

Heisenberg group H3 and special unitary group SU(2).

New methods for constructing a canal surface surrounding a biharmonic curve in the Lorentzian

Heisenberg group [Heis.

Roughly put (see the citation [15] for more details), if for an STGQ ([GAMMA], x, E), E is isomorphic to a general

Heisenberg group, then [GAMMA] is a flock quadrangle:

We will be interested in deformations of the discrete

Heisenberg group as a group acting properly discontinuously and cocompactly on a space X.

But many groups in physics such as the

Heisenberg group and also many applicable groups in engineering such as Motion groups are non-abelian and so that the standard STFT theory in abelian case fails.

Thanks to the magic (and obvious) relation between the 2n + 1-dimensional

Heisenberg group and its vector group [R.

In this paper we describe a method to derive a Weierstrass-type representation formula for simply connected immersed minimal surfaces in

Heisenberg group [H.

Turhan: Completeness of Lorentz Metric on 3-Dimensional

Heisenberg Group, Int.

Hans-Jurgen Eisler, who heads the DFG

Heisenberg group at the Light Technology Institute.

Ten chapters discuss the skew field of quaternions; elements of the geometry of S3, Hopf bundles, and spin representations; internal variables of singularity free vector fields in a Euclidean space; isomorphism classes, Chern classes, and homotopy classes of singularity free vector fields in 3-space; Heisenberg algebras,

Heisenberg groups, Minkowski metrics, Jordan algebras, and special linear groups; the Heisenbreg group and natural C*-algebras of a vector field in 3-space; the Schrodinger representation and the metaplectic representation; the

Heisenberg group as a basic geometric background of signal analysis and geometric optics; quantization of quadratic polynomials; and field theoretic Weyl quantization of a vector field in 3-space.

This

Heisenberg group has many important applications on Sub-Riemannian geometry and has very important role in physics.

Analysis of the Hodge Laplacian on the

Heisenberg Group