Lie-algebraic characterization of tangentially degenerate orbits of s-representations

AbstractIn this paper we study tangential degeneracy of the orbits of s-representations in the sphere. We show that the orbit of an s-representation is tangentially degenerate if and only if it is through a long root, or a short root of restricted root system of type G2. Moreover these orbits provide many new examples of tangentially degenerate submanifolds which satisfy the Ferus equality

Magnetic field effects on two-dimensional Kagome lattices

Magnetic field effects on single-particle energy bands (Hofstadter butterfly), Hall conductance, flat-band ferromagnetism, and magnetoresistance of two-dimensional Kagome lattices are studied. The flat-band ferromagnetism is shown to be broken as the flat-band has finite dispersion in the magnetic field. A metal-insulator transition induced by the magnetic field (giant negative magnetoresistance) is predicted. In the half-filled flat band, the ferromagnetic-paramagnetic transition and the metal-insulator one occur simultaneously at a magnetic field for strongly interacting electrons. All of the important magnetic fields effects should be observable in mesoscopic systems such as quantum dot superlattices.Comment: 10 pages, 4 figures, and 1 tabl

Poincaré formulas of complex submanifolds

We formulate Poincaré formulas of complex submanifolds in almost Hermitian homogeneous spaces, using Howard\u27s formulation of Poincaré formulas in Riemannian homogeneous spaces. This formula is an extension of Santaló\u27s one in complex space forms