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We consider several classes of symmetries of the Dirac Hamiltonian in 3+1 dimensions, with axially-deformed scalar and vector potentials. The symmetries include the known pseudospin and spin limits and additional symmetries which occur when…
In this paper we study the maximal subspaces of continuous n-homogeneous polynomials on complex and real non separable Banach spaces. In the real case we will prove that if P is a 2-homogeneous polynomial and if there exist a k-dimensional…
The question of whether a Sasakian metric can admit an additional compatible (K-)contact structure is addressed. In the complete case if the second structure is also assumed Sasakian, works of Tachibana-Yu and Tanno show that the manifold…
In this paper, we first give a convenient formula for bi-Laplacian on a sphere and the complete description of its eigenvalues, buckling eigenvalues, and their corresponding eigenfunctions. We then show that the radial (or rotationally…
This paper, we define the Mus-Gradient metric on tangent bundle $TM$ by a deformation non-conform of Sasaki metric over an n-dimensional Riemannian manifold $(M, g)$. First we investigate the geometry of the Mus-Gradient metric and we…
Supersymmetry is studied in 2+1 dimensions. In addition to the multiplets corresponding to those in 3+1 dimensions the Clifford algebra allows an extra set. When the extra chiral multiplet is included, formulating supersymmetric QED3 in the…
We construct consistent Kaluza--Klein reductions of D=11 supergravity to four dimensions using an arbitrary seven-dimensional Sasaki--Einstein manifold. At the level of bosonic fields, we extend the known reduction, which leads to minimal…
The conformal-bienergy functional $E_2^c$ is a modified version of the classical bienergy functional $E_2$ and it is conformally invariant in the case of a four-dimensional domain. The critical points of $E_2^c$ are called…
The main purpose of this paper is to give a mathematical definition of ``mirror symmetry'' for Calabi-Yau and G_2 manifolds. More specifically, we explain how to assign a G_2 manifold (M,\phi,\Lambda), with the calibration 3-form \phi and…
Every compact 3-Sasakian 7-manifold $M$ admits a canonical 2-parameter family of co-closed $\text{G}_2$-structures $\varphi_{a,b}$ for $a,b > 0$, as well as a foliation by $\varphi_{a,b}$-associative 3-folds whose leaf space $X$ is a…
Every closed, oriented, real analytic Riemannian 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, even as the real locus of an antiholomorphic, isometric involution. Every closed,…
We prove that every nearly Sasakian manifold of dimension greater than five is Sasakian. This provides a new criterion for an almost contact metric manifold to be Sasakian. Moreover, we classify nearly cosymplectic manifolds of dimension…
We classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four, and (2) between conformally-flat Riemannian manifolds of dimensions at least three.
We classify Lagrangian submanifolds of complex space forms, whose second fundamental form can be written in a certain way, depending on a real parameter. For some special values of this parameter, the resulting submanifolds are ideal in the…
The 2-parameter family of certain homogeneous Lorentzian 3-manifolds which includes Minkowski 3-space and anti-de Sitter 3-space is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group…
We first prove that, unlike the biharmonic case, there exist triharmonic curves with nonconstant curvature in a suitable Riemannian manifold of arbitrary dimension. We then give the complete classification of triharmonic curves in surfaces…
We introduce spin-harmonic structures, a class of geometric structures on Riemannian manifolds of low dimension which are defined by a harmonic unitary spinor. Such structures are related to SU(2) (dim=4,5), SU(3) (dim=6) and G_2 (dim=7)…
For any rank-one Riemannian symmetric space S of non-compact type and any discrete, cofinite, non-cocompact, torsion-free group $\Gamma$ of orientation-preserving Riemannian isometries on S, we develop a cohomological interpretation for the…
Inspired by the all-important conformal invariance of harmonic maps on two-dimensional domains, this article studies the relationship between biharmonicity and conformality. We first give a characterization of biharmonic morphisms,…
The space forms, the complex hyperbolic spaces and the quaternionic hyperbolic spaces are characterized as the harmonic manifolds with specific radial eigenfunctions of the Laplacian.