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By Otto Mutzbauer

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X; / where the first mapping is defined by the bundle pull back under the embedding S M ,! T Mn0, the second one by (12) and the third one by the identification . x; / D Jx , x 2 M. x; / 2 T Mn0. Ellipticity with Global Projection Conditions 2 53 In the following we formulate operators which appear as lower right corners of 2 matrices of the Toeplitz analogue of Boutet de Monvel’s calculus below. M; L1 / ! M; J2 / ! M; L2 /, respectively. MI J1 ; J2 /; 2 R, is called a Toeplitz operator of order 2 R associated with the projection data L1 ; L2 .

0; 0; t0 / D eij jto I, for all t0 2 R. Moreover, …j j is an irreducible unitary representation of Hn on the Hilbert space H. This can be easily seen by using the fact that … is an irreducible unitary representation of G on H. t u 4 Fourier Transforms and the Fourier Inversion Formula on G By the Stone-von Neumann theorem every irreducible unitary representation of G which acts non-trivially on the center is in fact unitarily equivalent to exactly one of , 2 Rm . Hence, the identification of f W 2 Rm g with Rm will be used.

W. Wong Abstract We compute the Riemannian curvature of the Heisenberg group and then contract it to the sectional curvature, Ricci curvature and the scalar curvature of the Heisenberg group. The main result so obtained is that the Heisenberg group is a space of constant positive scalar curvature. Keywords Heisenberg group • Left-invariant vector fields • Riemannian metric • Levi–Civita connection • Riemannian curvature • Sectional curvature • Ricci curvature • Scalar curvature Mathematics Subject Classification (2000).

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