Related papers: Isoparametric hypersurfaces in Randers space forms

A new class of harmonic Hadamard manifolds, those spaces called of hypergeometric type, is defined in terms of Gauss hypergeometric equations. Spherical Fourier transform defined on a harmonic Hadamard manifold of hypergeometric type admits…

The object of this paper is to introduce new classes of hypersurfaces of almost product-like statistical manifolds. The main properties and relations on $K-$para contact, para cosymplectic, para Sasakian and conformal hypersurfaces are…

We consider foliations of the whole three dimensional hyperbolic space H^3 by oriented geodesics. Let L be the space of all the oriented geodesics of H^3, which is a four dimensional manifold carrying two canonical pseudo-Riemannian metrics…

In this paper, we investigate a holonomy invariant elliptic anisotropic surface energy for hypersurfaces in a complete Riemannian manifold, where "holonomy invariant" means that the elliptic parametric Lagrangian (i.e., a Finsler metric) of…

It is well known that simply connected symmetric spaces of non-positive sectional curvature admit a linear isoperimetric filling inequality for cycles of dimension greater than or equal to the rank of the space. In this note we extend that…

In this paper, almost product-like Riemannian manifolds are investigated. Basic properties on tangential hypersurfaces of almost product-like Riemannian manifolds are obtained. Some examples of tangential hypersurfaces are presented. Some…

In any closed smooth Riemannian manifold of dimension at least three, we use the min-max construction to find anisotropic minimal hyper-surfaces with respect to elliptic integrands, with a singular set of codimension~$2$ vanishing Hausdorff…

We provide integral formulae for the ADM mass of asymptotically flat hypersurfaces in Riemannian manifolds with a certain warped product structure in a neighborhood of infinity, thus extending Lam's recent results on Euclidean graphs to…

In (equi-)affine differential geometry, the most important algebraic invariants are the affine (Blaschke) metric h, the affine shape operator S and the difference tensor K. A hypersurface is said to admit a pointwise symmetry if at every…

Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…

We give necessary and sufficient conditions for a semi-Riemannian manifold of arbitrary signature to be locally isometrically immersed into certain warped products. Then, we describe a way to use the structure equations of such immersions…

Riemannian geodesic orbit spaces (G/H,g) are natural generalizations of symmetric spaces, defined by the property that their geodesics are orbits of one-parameter subgroups of G. We study the geodesic orbit spaces of the form (G/S,g), where…

Let $M^n$ be an $n$-dimensional umbilic-free hypersurface in the $(n+1)$-dimensional Lorentzian space form $M^{n+1}_1(c)$. Three basic invariants of $M^n$ under the conformal transformation group of $M^{n+1}_1(c)$ are a $1$-form $C$, called…

In this paper we argue that when gauge invariance is taken into consideration, there is no consistent geometric framework of Finsler class that can accommodate Randers type spaces. In this context, an alternative non-Finslerian framework…

Assuming minimal regularity assumptions on the data, we revisit the classical problem of finding isometric immersions into the Minkowski spacetime for hypersurfaces of a Lorentzian manifold. Our approach encompasses metrics having Sobolev…

We continue our study [Ou4] of f-biharmonic maps and f-biharmonic submanifolds by exploring the applications of f-biharmonic maps and the relationships among biharmonicity, f-biharmonicity and conformality of maps between Riemannian…

The set of matrix tuples with invariant subspaces whose dimensions sum up to the dimension of the space, but which do not span the whole space form an algebraic hypersurface. We found the equation of this hypersurface. This generalizes…

We classify hypersurfaces of rank two of Euclidean space $\R^{n+1}$ that admit genuine isometric deformations in $\R^{n+2}$. That an isometric immersion $\hat f\colon\,M^n\to\R^{n+2}$ is a genuine isometric deformation of a hypersurface…

In this paper we develop the notion of screen isoparametric hypersurface for null hypersurfaces of Robertson-Walker spacetimes. Using this formalism we derive Cartan identities for the screen principal curvatures of null screen…

We show the existence of isometric (or Ford) fundamental regions for a large class of subgroups of the isometry group of any rank one Riemannian symmetric space of noncompact type. The proof does not use the classification of symmetric…