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en: Eigenvalues associated with a periodic orbit of the magnetic flow

en: This paper concerns with a relationship between classical orbits and quantum energies for the dynamical system in a magnetic field. It is shown that there exist approximate quantum energies associated with a classical periodic orbit which satisfies a "quatization condition".

en: Contemporary Mathematics

ja: Contemporary Mathematics


en: Difference spectrum of the Schrodinger operator in a magnetic field

en: Mathematische Zeitschrift

ja: Mathematische Zeitschrift


en: Lax-type isospectral deformations on nilmanifolds

en: Annals of Global Analysis and Geometry

ja: Annals of Global Analysis and Geometry


en: Spectra and geodesic flows on nilmanifolds --- Reductions of Hamiltonian systems and differential operators

en: Journal of Mathematical Society of Japan


en: Isospectral connections on line bundles

ja: Isospectral connections on line bundles


en: Spectrum of the Schrodinger operator on a line bundle over complex projective spaces

en: Tohoku Mathematical Journal

ja: Tohoku Mathematical Journal


en: Spectrum of the Laplacian on vector bundles over C2π-manifolds

en: Journal of Differential Geometry

ja: Journal of Differential Geometry


en: Band asymptotics of eigenvalues for the Zoll manifold

en: Letters in Mathematical Physics

ja: Letters in Mathematical Physics


en: A note on quantization of a free particle in the Zoll manifold


en: Some spectral results for the Laplacian on line bundles over Sn

en: Commentarii Mathematici Helvetici

ja: Commentarii Mathematici Helvetici


en: Spectrum and holonomy of the line bundle over the sphere


en: Time-dependent mechanical symmetries and extended Hamiltonian systems

en: Reports on Mathematical Physics

ja: Reports on Mathematical Physics


en: On isospectral deformations of Riemannian metrics. II

en: Compositio Mathematica

ja: Compositio Mathematica


en: On isospectral deformations of Riemannian metrics


en: On the characterization of flat metrics by the spectrum


en: Spectral invariants of linear differential operators and conservation laws of nonlinear equations

en: Mathematica Japonica

ja: Mathematica Japonica


en: On the symmetry algebra of the Schrodinger wave equation


en: Numbers associated to symmetric differential operators and the Bernoulli numbers

en: By considering a certain symmetric differential operator we introducea sequence of numbers fCkg1k=0, and clarify their properties, which aresimilar to those of the Bernoulli numbers. It is shown that the generatingfunction of fCkg is the hyperbolic tangent function, and some (maybeknown) properties of the Bernoulli numbers are derived through those ofCk.

en: Journal of Mathematics, The University of Tokushima


en: On a classical-quantum correspondence for mechanics in a gauge field

en: This paper studies the classical and the quantum mechanics in a non-abelian gauge eld on the basis of the symplectic geometry and the theoryof representation of Lie groups. As a classical-quantum correspondencewe present a conjecture on the quasi-mode corresponding to a certainclassical energy level.

ja: Journal of Mathematics, The University of Tokushima


en: A note on symmetric differential operators and binomial coefficients

en: In this note we derive some identities concerning the binomial coefficients by considering a certain n-th order symmetric differential operatoron Rm associated to the function p(x，ξ)(x ∈ Rm) which is a homogeneouspolynomial in ξ.


en: A note on a heat invariant and the Ricci flow on surfaces

en: In this short note，we consider the monotonicity of the heat invarianta2 (g) for a Riemannian metric g under the normalized Ricci flow on aclosed surface. We show that a2(g(t)) is decreasing under the normalizedRicci flow g(t) in the space of metrics of non-positive curvature.


en: A Geometrical Formulation for Classical Mechanics in Gauge Fields

en: We give a geometrical formulation for the classical mechanics in a non-abelian gauge field on a Riemannian manifold. The formulation is based on the reduction procedure associated to the non-abelian symmetry in the principal bundle which describes the gauge field. In the formulation we present explicitly the equation of the motion (called Wong's equation) of a charged particle by using a local coordinate system.


en: On Maslov's quantization condition for mechanics in a magnetic field

en: Journal of Mathematics, Tokushima University


en: Correction and addendum to: On the classical and the quantum mechanics in a magnetic field

ja: Journal of Mathematics, Tokushima University


en: On the classical and the quantum mechanics in a magnetic field


en: A note on the deformations of Hamiltonian systems on nilmanifolds


en: On spectra of the Laplacian on vector bundles