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The trace of the generalized harmonic oscillator

Jared Wunsch (1999)

Annales de l'institut Fourier

We study a geometric generalization of the time-dependent Schrödinger equation for the harmonic oscillator D t + 1 2 Δ + V ψ = 0 ( 0 . 1 ) where Δ is the Laplace-Beltrami operator with respect to a “scattering metric” on a compact manifold M with boundary (the class of scattering metrics is a generalization of asymptotically Euclidean metrics on ℝ n , radially compactified to the ball) and V is a perturbation of 1 2 ω 2 x - 2 , with x a boundary defining function for M (e.g. x = 1 / r in the compactified Euclidean case). Using the quadratic-scattering...

Traceless component of the conformal curvature tensor in Kähler manifold

Shoichi Funabashi, Hyang Sook Kim, Y.-M. Kim, Jin Suk Pak (2006)

Czechoslovak Mathematical Journal

We investigate the traceless component of the conformal curvature tensor defined by (2.1) in Kähler manifolds of dimension ≥ 4 , and show that the traceless component is invariant under concircular change. In particular, we determine Kähler manifolds with vanishing traceless component and improve some theorems (for example, [4, pp. 313–317]) concerning the conformal curvature tensor and the spectrum of the Laplacian acting on p ...

Twistor forms on Kähler manifolds

Andrei Moroianu, Uwe Semmelmann (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Twistor forms are a natural generalization of conformal vector fields on riemannian manifolds. They are defined as sections in the kernel of a conformally invariant first order differential operator. We study twistor forms on compact Kähler manifolds and give a complete description up to special forms in the middle dimension. In particular, we show that they are closely related to hamiltonian 2-forms. This provides the first examples of compact Kähler manifolds with non–parallel twistor forms in...

Two new estimates for eigenvalues of Dirac operators

Wenmin Gong, Guangcun Lu (2016)

Annales Polonici Mathematici

We establish lower and upper eigenvalue estimates for Dirac operators in different settings, a new Kirchberg type estimate for the first eigenvalue of the Dirac operator on a compact Kähler spin manifold in terms of the energy momentum tensor, and an upper bound for the smallest eigenvalues of the twisted Dirac operator on Legendrian submanifolds of Sasakian manifolds. The sharpness of those estimates is also discussed.

Two remarks on Riemann surfaces.

José M. Rodriguez (1994)

Publicacions Matemàtiques

We study the relationship between linear isoperimetric inequalities and the existence of non-constant positive harmonic functions on Riemann surfaces.We also study the relationship between growth conditions of length of spheres and the existence and the existence of Green's function on Riemann surfaces.

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