61 research outputs found
The Lichnerowicz theorem on CR manifolds
We obtain a Bochner type formula and an estimate from below on the spectrum
of the sublaplacian of a compact strictly pseudoconvex CR manifold.Comment: 21 page
On the boundary behavior of the holomorphic sectional curvature of the Bergman metric
We obtain a conceptually new differential geometric proof of P.F. Klembeck's
result that the holomorphic sectional curvature of a strictly pseudoconvex
domain approaches (in the boundary limit) the constant sectional curvature of
the Bergman metric of the unit ball.Comment: 14 page
On the pseudohermitian sectional curvature of a strictly pseudoconvex CR manifold
We study the pseudohermitian sectional curvature of a CR manifold.Comment: 29 page
Jacobi fields of the Tanaka-Webster connection on Sasakian manifolds
We build a variational theory of geodesics of the Tanaka-Webster connection
on a strictly pseudoconvex CR manifold.Comment: 52 page
Kostant-Souriau-Odzijewicz quantization of a mechanical system whose classical phase space is a Siegel domain
On the canonical foliation of an indefinite locally conformal Kähler manifold with a parallel Lee form
We study the semi-Riemannian geometry of the foliation of an indefinite locally conformal Kähler (l.c.K.) manifold , given by the Pfaffian equation , provided that and ( is the Lee form of ). If is conformally flat then every leaf of is shown to be a totally geodesic semi-Riemannian hypersurface in , and a semi-Riemannian space form of sectional curvature , carrying an indefinite c-Sasakian structure (in the sense of T. Takahasi). As a corollary of the result together with a semi-Riemannian version of the de Rham decomposition theorem (due to H. Wu) any geodesically complete, conformally flat, indefinite Vaisman manifold of index , 0 < s < n, is locally biholomorphically homothetic to an indefinite complex Hopf manifold , 0 < lambda < 1, equipped with the indefinite Boothby metric
On Schwarzschild's interior solution and perfect fluid star model
We solve the boundary value problem for Einstein’s gravitational field equations in the presence of matter in the form of an incompressible perfect fluid of density rho and pressure field p(r) located in a ball r leq r_0. We find a 1-parameter family of time-independent and radially symmetric solutions {(g_a, rho_a, p_a) : -2m < a < 9 kappa M/(4c^2) identifies the “physical” (i.e., such that p_a(r) geq 0 and p_a(r) is bounded in 0 leq r leq r_0) solutions {p_a : a in mathcal{U}_0} for some neighbourhood mathcal{U}_0 subset (-2m , +infty) of a = 0. For every star model {g_a : a_0 < a < a_1}, we compute the volume V(a) of the region r leq r_0 in terms of abelian integrals of the first, second, and third kind in Legendre form
Beltrami equations on Rossi spheres
Beltrami equation on (where , , are the Rossi operators i.e., spans the globally nonembeddable CR structure on discovered by H. Rossi) are derived such that to describe quasiconformal mappings from the Rossi sphere . Using the Greiner-Kohn-Stein solution to the Lewy equation and the Bargmann representations of the Heisenberg group, we solve the Beltrami equations for Sobolev-type solutions such that with
Yang-Mills fields on CR manifolds
We study pseudo Yang-Mills fields on a compact strictly pseudoconvex CR
manifold.Comment: 52 page
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