When G is a complex reductive algebraic group and G/K is a reductive symmetric space, the decomposition of C[G/K] as a K-module was obtained (in a non-constructive way) by Richardson, generalizing the celebrated result of Kostant-Rallis for the linearized problem (the harmonic decomposition of the isotropy representation). To obtain a constructive version of Richardson’s results, this paper stu...

Jost and Zuo’s theorem (adapting an earlier idea of Gromov [7]) states that if the Kähler form ω on a complete Kähler manifold satisfies ω = dβ, where β is a one-form of linear growth, then the only L harmonic forms lie in the middle dimension. An application of the same argument shows further that if G is a connected Lie group of isometries on a complete Riemannian manifold generated by Killin...

We show that relativistic mean fields theories with scalar, S, and vector, V , quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry and positive energy bound states when S = −V . The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this symmetry by introducin...

We present dyonic BPS static black hole solutions for general d = 4, N = 2 supergravity theories coupled to vector and hypermultiplets. These solutions are generalisations of the spherically symmetric Majumdar-Papapetrou black hole solutions of Einstein-Maxwell gravity and are completely characterised by a set of constrained harmonic functions. In terms of the underlying special geometry, these...

In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...

Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as " conformal " transports and investigated over (Ln, g)-spaces. They are more general than the Fermi-Walker transports. In an analogous way as in the case of Fermi-Walker transports a conformal covariant differential operator and its conformal der...

recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. using this machinery, we have defined the concept of symmetric curvature. this concept is natural and is related to the notions divergence and laplacian of vector fields. this concept is also related to the derivations on the algebra of symmetric forms which has been discus...

In this paper the Berry and Aharonov-Bohm phases are generalized to nonlinear topological phase fields on pseudospheres, where the coordinate vector field is parallel transported along the signal/soliton vector field with Levi–Civita connection. Projective PSL(2,R) symmetry describes the relativistic self-interacting bosonic sine-Gordon field. A Coulomb potential can be induced as the stereogra...