相关论文: Nullity distributions on real hypersurfaces in non…

New fixed point results are presented for ${\cal U}_c^{\kappa}(X,X)$ maps in extension type spaces.

In [7], Guan, Ren and Wang obtained a $C^2$ a priori estimate for admissible 2-convex hypersurfaces satisfying the Weingarten curvature equation $\sigma_2(\kappa(X))=f(X, \nu(X)).$ In this note, we give a simpler proof of this result, and…

We give the explicit form of the half-string representation in the continuous kappa basis. We show the comma structure of the three-vertex, when expanded around an arbitrary projector, and that the zero-mode must be replaced by the…

Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We describe relations between singular complex analytic vector fields…

This paper investigates the isomorphisms between principal distributions $\mathcal{D}_k$ $(k=1,\dots 4)$ on OT--FKM type isoparametric hypersurfaces in spheres. We recover the isomorphism $\mathcal{D}_1 \cong \mathcal{D}_3$ established by…

In a metric $g.f.f$-manifold we study lightlike hypersurfaces $M$ tangent to the characteristic vector fields, and owing to the presence of the $f$-structure, we determine some decompositions of $TM$ and of a chosen screen distribution…

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…

We introduce and study the vanishing homology of singular projective hypersurfaces. We prove its concentration in two levels in case of 1-dimensional singular locus $\Sigma$, and moreover determine the ranks of the nontrivial homology…

We classify the non-degenerate homogeneous hypersurfaces in real and complex affine four-space whose symmetry group is at least four-dimensional.

Let $V$ be a finite dimensional vector space over a local field $F$. Let $\chi: F^\times \rightarrow \mathbb C^\times$ be an arbitrary character of $F^\times$. We determine the structure of the natural representation of $\mathrm{GL}(V)$ on…

The subject of this paper is the investigation of inflationary non-Gaussianities of the local type with extreme value statistics of the weak lensing convergence kappa. Specifically, we describe the influence of inflationary…

We introduce a (bi)category $\mathfrak{Sing}$ whose objects can be functorially assigned spaces of distributions and generalized functions. In addition, these spaces of distributions and generalized functions possess intrinsic notions of…

This paper studies the application of multimomentum maps to the constraint analysis of general relativity on null hypersurfaces. It is shown that, unlike the case of spacelike hypersurfaces, some constraints which are second class in the…

We investigate the complex analytic structure of the complement of a non-singular hypersurface with unitary flat normal bundle when the corresponding line bundle admits a Hermitian metric with semipositive curvature.

We establish the asymptotic regularity and the $\Delta$-convergence of the sequence constructed by the alternating projections to closed convex sets in a CAT($\kappa$) space with $\kappa > 0$. Furthermore, the strong convergence of the…

We provide normal forms for singularities of analytic hypersurfaces in $({\mathbb C}^n,0)$, using holomorphic vector fields.

We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.

We describe the structure of the singular sets of constant curvature, convex hypersurfaces in hyperbolic space for general convex curvature functions. We apply this result to the study of the ideal Plateau problem in hyperbolic space for…

We classify singular holomorphic vector fields in two-dimensional complex space admitting a (Levi-nonflat) real-analytic invariant 3-fold through the singularity. In this way, we complete the classification of infinitesimal symmetries of…

For appropriately values of $H$, we obtain an area estimate for a complete non-compact $H$-surface of finite topology and finite area, embedded in a three-manifold of negative curvature. Moreover, in the case of equality and under…