Related papers: On the equiaffine symmetric hyperspheres

This paper is concerned with the completeness (with respect to the centroaffine metric) of hyperbolic centroaffine hypersurfaces which are closed in the ambient vector space. We show that completeness holds under generic regularity…

In this paper, we show that any 3-dimensional normal affine quasihomogeneous SL(2)-variety can be described as a categorical quotient of a 4-dimensional affine hypersurface. Moreover, we show that the Cox ring of an arbitrary 3-dimensional…

The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for…

We study here systems of symmetries on $|1|$--graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous $|1|$--graded geometries. We show the existence of an invariant admissible…

Locally harmonic manifolds are Riemannian manifolds in which small geodesic spheres are isoparametric hypersurfaces, i.e., hypersurfaces whose nearby parallel hypersurfaces are of constant mean curvature. Flat and rank one symmetric spaces…

We establish estimates for the number of solutions of certain affine congruences. These estimates are then used to prove Manin's conjecture for a cubic surface split over Q and whose singularity type is D_4. This improves on a result of…

Building on work of Furstenberg and Tzkoni, we introduce ${\bf r}$-flag affine quermassintegrals and their dual versions. These quantities generalize affine and dual affine quermassintegrals as averages on flag manifolds (where the…

We wish to attack the problems that H.~Anciaux and K.~Panagiotidou posed in [1], for non-degenerate real hypersurfaces in indefinite complex projective space. We will slightly change these authors' point of view, obtaining cleaner equations…

The equivariant cohomology of certain moduli spaces of sheaves on isotrivial elliptic surfaces are shown to admit representations of infinite dimensional Lie (super)algebras. The construction is based on work of Billig and Chen-Li-Tan on…

In this paper, we mainly prove a theorem with a corollary establishing two characterizations of the Calabi composition of hyperbolic hyperspheres, where the second characterization (i.e., the corollary) has been given via a dual…

This paper explores equi-centro-affine extremal hypersurfaces in an ellipsoid. By analyzing the evolution of invariant submanifold flows under centro-affine unimodular transformations, we derive the first and second variational formulas for…

We provide a framework to classify hyperbolic monopoles with continuous symmetries and find a Structure Theorem, greatly simplifying the construction of all those with spherically symmetry. In doing so, we reduce the problem of finding…

In this paper, I prove a splitting theorem for equifocal submanifolds with non-flat section in a simply connected symmetric space of compact type. Also, by using the splitting theorem, I prove that the sections of equifocal submanifolds…

We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in $\mathbb{R}^3$. We find that several surfaces,…

In this paper we use the relationship between conformal metrics on the sphere and horospherically convex hypersurfaces in the hyperbolic space for giving sufficient conditions on a conformal metric to be radial under some constrain on the…

A smooth hypersurface over a finite field $\mathbb{F}_q$ is called Frobenius nonclassical if the image of every geometric point under the $q$-th Frobenius endomorphism remains in the unique hyperplane tangent to the point. In this paper, we…

In this paper we study the existence of special symmetric solutions to a Hamiltonian hyperbolic-hyperbolic coupled spin-field system, where the spins are maps from $\mathbb R^{2+1}$ into the sphere $\S^2$ or the pseudo-sphere $\H^2$. This…

We prove that equivariant, holomorphic embeddings of Hermitian symmetric spaces are totally geodesic (when the image is not of exceptional type).

We develop a general framework for the quantization of bosonic and fermionic field theories on affine bundles over arbitrary globally hyperbolic spacetimes. All concepts and results are formulated using the language of category theory,…

We prove that any finitely smooth axially symmetric strictly convex domain, with everywhere positive curvature and sufficiently close to an ellipse is area spectrally rigid. This means that any area-isospectral family of domains in this…