Related papers: Minimal two-spheres with constant curvature in the…

We construct three kinds of complete embedded minimal surfaces in $\Bbb H^2\times \Bbb R$. The first is a simply connected, singly periodic, infinite total curvature surface. The second is an annular finite total curvature surface. These…

I classify the Finsler structures on the 2-sphere that have constant Finsler-Gauss curvature and whose geodesics are the great circles. Modulo diffeomorphism, there is a 2-parameter family of such Finsler structures, only one of which is…

It was proved in the first part of this work \cite{0} that Stolarsky's invariance principle, known previously for point distributions on the Euclidean spheres \cite{33}, can be extended to the real, complex, and quaternionic projective…

We prove ``half-space" intersection properties in three settings: the hemisphere, half-geodesic balls in space forms, and certain subsets of Gaussian space. For instance, any two embedded minimal hypersurfaces in the sphere must intersect…

A subvariety of a complex projective space has a well-known dual variety, which is the set of its tangent hyperplanes. The purpose of this paper is to generalise this notion for a subvariety of a quite general partial flag variety. A…

In this work an intrinsic projectively invariant distance is used to establish a new approach to the study of projective geometry in Finsler space. It is shown that the projectively invariant distance previously defined is a constant…

We prove the regularity of cohomogeneity two equivariant isotopy minimization problems. Based on this, we develop cohomogeneity two equivariant min-max theory for minimal hypersurfaces proposed by Pitts and Rubinstein in 1988. As an…

We investigate several classes of submanifolds of almost quaternionic skew-Hermitian manifolds $(M^{4n}, Q, \omega)$, including almost symplectic, almost complex, almost pseudo-Hermitian and almost quaternionic submanifolds. In the…

We propose a formulation of the quantization problem of Manin quadruples, and show that a solution to this problem yields a quantization of the corresponding Poisson homogeneous spaces. We then solve both quantization problems in an example…

In this article, we use the harmonic sequence associated to a weakly conformal harmonic map $f:S\to S^6$ in order to determine explicit examples of linearly full almost complex 2-spheres of $S^6$ with at most two singularities. We prove…

Let $M$ be a complete Riemannian $3$-manifold with sectional curvatures between $0$ and $1$. A minimal $2$-sphere immersed in $M$ has area at least $4\pi$. If an embedded minimal sphere has area $4\pi$, then $M$ is isometric to the unit…

We present a necessary and sufficient condition for the strict positive definiteness of a real, continuous, isotropic and positive definite kernel on a two-point compact homogeneous space. The characterization adds to others previously…

A new integrable generalization to the 2D sphere $S^2$ and to the hyperbolic space $H^2$ of the 2D Euclidean anisotropic oscillator Hamiltonian with Rosochatius (centrifugal) terms is presented, and its curved integral of the motion is…

The minimal model program suggests a compactification of the moduli space of hyperplane arrangements which is a moduli space of stable pairs. Here, a stable pair consists of a scheme X which is a degeneration of projective space and a…

In this paper, we study diagonal maps between spheres given by two homogeneous polynomial maps between spheres, defined on the same domain sphere. First we find their bitension field, then we give a method for generating proper biharmonic…

An affine hypersurface $M$ is said to admit a pointwise symmetry, if there exists a subgroup $G$ of ${\rm Aut}(T_p M)$ for all $p\in M$, which preserves (pointwise) the affine metric $h$, the difference tensor $K$ and the affine shape…

We extend Jordan's notion of principal angles to work for two subspaces of quaternionic space, and so have a method to analyze two orthogonal projections in M_n(A) for A the real, complex or quaternionic field (or skew field). From this we…

We study existence and non-existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all critical points of the Hilbert-Einstein functional…

The constant curvature analogue on the two-dimensional sphere and the hyperbolic space of the integrable H\'enon-Heiles Hamiltonian $\mathcal{H}$ given by $$ \mathcal{H}=\dfrac{1}{2}(p_{1}^{2}+p_{2}^{2})+ \Omega \left(q_{1}^{2}+ 4…

We investigate horospherical homogeneous spaces--a class of spherical homogeneous spaces encompassing both flag varieties and algebraic tori--over fields of characteristic p>0, and establish their complete classification for p>2.