arXiv research

The paper studies half-lightlike submanifolds in Lorentzian manifolds with specific distributions.

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 hypersurfaces in Lorentzian space forms and provide a local characterization of such hypersu…

Study Einstein warped-product manifolds with specific curvature conditions.

A pp-wave is a Lorentzian manifold with a parallel light-like vector field satisfying a certain curvature condition. We introduce generalisations of pp-waves, on one hand by allowing the vector field to be recurrent and on the other hand by weakening the curvature condition. These generalisations are related to the scr…

New types of null hypersurfaces found in Sasakian space-forms.

Study on null hypersurfaces in complex contact manifolds.

Study on special null submanifolds in indefinite Sasakian manifolds.

Study of null hypersurfaces in semi-Riemannian manifolds with applications.

Study on umbilical submanifolds in specific geometric spaces.

Novel approximation hierarchy for sparse quadratic programs.

We derive total mean curvature integration formulae of a three co-dimensional foliation $\mathcal{F}^{n}$ on a screen integrable half-lightlike submanifold, $M^{n+1}$ in a semi-Riemannian manifold $\overline{M}^{n+3}$. We give generalized differential equations relating to mean curvatures of a totally umbilical half-li…

The paper classifies and determines properties of specific hypersurfaces in complex hyperbolic quadrics.

Study on isoparametric and constant-curvature hypersurfaces in Finsler spaces.

Study on discrete surfaces with constant principal curvature for nanocarbon applications.

Study behavior of curvatures near singular points of frontals.

Study on hypersurfaces with specific curvature conditions.

Classifies surfaces with special curvature properties.

The paper studies Einstein hypersurfaces in a specific warped product space.

Study the geometry of a surface formed by extending a Whitney umbrella.

In this paper are determined the principal curvatures and principal curvature lines on canal surfaces which are the envelopes of families of spheres with variable radius and centers moving along a closed regular curve in R^3. By means of a connection of the differential equations for these curvature lines and real Ricc…

The paper classifies Hopf hypersurfaces with constant curvatures on complex quadrics.

The study examines principal directions and curvatures of Lagrangian submanifolds.

We consider convex hypersurfaces for which the ratio of principal curvatures at each point is bounded by a function of the maximum principal curvature with limit 1 at infinity. We prove that the ratio of circumradius to inradius is bounded by a function of the circumradius with limit 1 at zero. We apply this result to …

If $M$ is an isoparametric hypersurface in a sphere $S^n$ with four distrinct principal curvatures, then the principal curvatures $κ_1,...,κ_4$ can be ordered so that their multiplicities satisfy $m_1=m_2$ and $m_3=m_4$, and the cross-ratio $r$ of the principal curvatures (the Lie curvature) equals -1. In this paper, w…

Study disproves a conjecture about constant curvature hypersurfaces.

Researchers compute differential invariants for Carrollian spacetimes.

The purpose of the present work is to study (marginally) trapped submanifolds lying in a null hypersurface. Let $(M,g,N)\to\Bm(c)$ be a null hypersurface of a space-time with constant sectional curvature $c$, endowed with a Screen Integrable and Conformal rigging $N$. The (Marginally) Trapped Submanifolds we are intere…

The paper constructs all cmc hypersurfaces with two principal curvatures.

The paper shows nearly-Fuchsian properties for certain hyperbolic 3-manifolds.

In this paper, we have studied biharmonic hypersurfaces in space form $\bar{M}^{n+1}(c)$ with constant sectional curvature $c$. We have obtained that biharmonic hypersurfaces $M^{n}$ with at most three distinct principal curvatures in $\bar{M}^{n+1}(c)$ has constant mean curvature. We also obtain the full classificatio…

Study surfaces with constant ratio of principal curvatures in Euclidean and isotropic geometries.

Lie minimal surfaces are characterized by differential equations of principal curvatures.

Principal binets generalize curvature line surfaces to square lattices and are a discrete integrable system.

We find the first examples of real hypersurfaces with two nonconstant principal curvatures in complex projective and hyperbolic planes, and we classify them. It turns out that each such hypersurface is foliated by equidistant Lagrangian flat surfaces with parallel mean curvature or, equivalently, by principal orbits of…

We classify all real hypersurfaces with constant principal curvatures in the complex hyperbolic plane.

The paper proves a stronger Petersen--Wilhelm conjecture for principal bundles.

The study examines connections and their curvatures on different types of bundles.

We study principal curvatures of fibers and Heegaard surfaces smoothly embedded in hyperbolic 3-manifolds. It is well known that a fiber or a Heegaard surface in a hyperbolic 3-manifold cannot have principal curvatures everywhere less than one in absolute value. We show that given an upper bound on the genus of a minim…

We consider surfaces in Euclidean space parametrized on an annular domain such that the first fundamental form and the principal curvatures are rotationally invariant, and the principal curvature directions only depend on the angle of rotation (but not the radius). Such surfaces generalize the Enneper surface. We show …

We study surfaces with one constant principal curvature in Riemannian and Lorentzian three-dimensional space forms. Away from umbilic points they are characterized as one-parameter foliations by curves of constant curvature, each of these curves being centered at a point of a regular curve and contained in its normal p…

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

The study examines spacelike hypersurfaces in Minkowski space with constant $σ_{n-1}$ curvature.

The study classifies hypersurfaces with constant principal curvatures in $\mathbb{S}^3 imes \mathbb{R}$ and $\mathbb{H}^3 imes \mathbb{R}$.

The paper characterizes surfaces using invariants.

The paper proves properties of triharmonic CMC hypersurfaces with specific curvature conditions.

RaSE screens variables via random subspaces, identifying joint effects.

Classifies hypersurfaces with specific curvature properties in 4D space.

We classify the homogeneous and isoparametric hypersurfaces of $\mathbb{S}^2\times\mathbb{S}^2$. In the classification, besides the hypersurfaces $\mathbb{S}^1(r)\times\mathbb{S}^2,\,r\in (0,1]$, it appears a family of hypersurfaces with three different constant principal curvatures and zero Gauss-Kronecker curvature. …