arXiv research

Study classifies submanifolds in probability simplex.

The study classifies totally umbilical surfaces in warped product manifolds.

Characterizes totally umbilical hypersurfaces in product spaces.

The purpose of this paper is to classify totally umbilical slant submanifolds of a Kenmotsu manifold. We prove that a totally umbilical slant submanifold $M$ of a Kenmotsu manifold $\bar M$ is either invariant or anti-invariant or $dim M=1$ or the mean curvature vector $H$ of $M$ lies in the invariant normal subbundle.…

Totally umbilic surfaces in hyperbolic 3-manifolds are constructed and characterized.

We obtain an exhaustive classification of totally umbilical surfaces in unimodular and non-unimodular simply-connected 3-dimensional Lie groups endowed with arbitrary left-invariant Riemannian metrics. This completes the classification of totally umbilical surfaces in homogeneous Riemannian 3-manifolds.

Characterizes curves in totally umbilical surfaces of space forms.

We get obstructions to existence of semi-Riemannian submersions with totally umbilic fibres.

We get obstructions to existence of semi-Riemannian submersions with totally umbilic fibres.

Totally umbilical hypersurfaces in Spin^c manifolds with special spinors have constant mean curvature.

We show that there is a correspondence between totally umbilic null hypersurfaces in generalized Robertson-Walker spaces and twisted decompositions of the fibre. This allows us to prove that nullcones are the unique totally umbilic null hypersurfaces in the closed Friedmann Cosmological model. We also apply this kind o…

Study totally umbilic submanifolds using planar pseudo-geodesics.

The paper classifies submanifolds in pseudo-Riemannian space forms.

Study of $f$-biharmonic hypersurfaces in conformally flat spaces.

Study of hypersurfaces in Sol4_0 geometry, classifying parallel and totally umbilical types.

Study null energy condition impacts on special hypersurfaces in static spacetimes.

We discuss two kinds of almost contact metric structures on a one-parameter family of totally umbilical hyperspheres in the nearly Kaehler unit 6-sphere.

The aim of this short article is to investigate the possibility of existence of totally umbilical isometric immersions in R^3 with isothermal parametrization and harmonic metric.

We study non-degenerate, totally umbilical surfaces of a special class of pseudo-Riemannian manifolds, namely Walker three-manifolds. We show that such surfaces are either one of a totally geodesic family described by Calvaruso and Van der Veken or the ambient manifold must be locally conformally flat (here the surface…

We prove that a Riemannian product of type M x R (where R denotes the Euclidean line) admits totally umbilical hypersurfaces if and only if M has locally the structure of a warped product and we give a complete description of the totally umbilical hypersurfaces in this case. Moreover, we give a necessary and sufficient…

Study on real hypersurfaces in products of complex space forms, proving rigidity and nonexistence results.

We prove that a totally umbilical biharmonic surface in any $3$-dimensional Riemannian manifold has constant mean curvature. We use this to show that a totally umbilical surface in Thurston's 3-dimensional geometries is proper biharmonic if and only if it is a part of $S^2(1/\sqrt{2})$ in $S^3$. We also give complete c…

Study on null helices in semi-Riemannian manifolds with special submanifolds.

We present classifications of totally geodesic and totally umbilical Legendrian submanifolds of $(κ,μ)$-spaces with Boeckx invariant $I \leq -1$. In particular, we prove that such submanifolds must be, up to local isometries, among the examples that we explicitly construct.

Study proves a new formula for capillary hypersurfaces and shows a flow converging to a special shape.

We discuss existence and classification of totally umbilic surfaces in the model geometries of Thurston and the Berger spheres. We classify such surfaces in $H^2 \times R$, $S^2 \times R$ and the Sol group. We prove nonexistence in the Berger spheres and in the remaining model geometries other than the space forms.

Following ideas of Choe and Fernandez-do Carmo, we give sufficient conditions for a disk type surface, with piecewise smooth boundary, to be totally umbilical for a given Coddazi pair. As a consequence, we obtain rigidity results for surfaces in space forms and in homogeneous product spaces that generalizes some known …

Explicit formulas for extrinsic Paneitz operators and Q-curvatures for totally umbilic hypersurfaces.

New inequality shows all special submanifolds in light cone are totally umbilical spheres.

The study examines spacelike foliations on Lorentz manifolds under specific conditions.

The paper finds conditions for certain hypersurfaces to be totally umbilical.

A spacelike surface in four-dimensional Lorentz-Minkowski spacetime through the lightcone has a meaningful lightlike normal vector field $η$. Several sufficient assumptions on such a surface with non-degenerate $η$-second fundamental form are established to prove that it must be a totally umbilical round sphere. With t…

The paper studies biharmonic conformal hypersurfaces in Riemannian manifolds.

In this paper we study curvature properties of semi-symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,\widetilde g)$ of a Kähler-Norden manifold $(\overline M,\overline J,\overline g,\overline {\widetilde g})$ of constant totally real sectional curvatures $\overline ν$ and …

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…

Study Clairaut anti-invariant submersions on nearly Kaehler manifolds.

Study on umbilical submanifolds in specific geometric spaces.

Totally geodesic Lagrangian submanifolds in nearly Kähler S³×S³.

The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.

Characterizes spacetimes using doubly torqued vectors.

In this note, we give a geometric characterization of the compact and totally umbilical hypersurfaces that carry a non trivial locally static Killing Initial Data (KID). More precisely, such compact hypersurfaces have constant mean curvature and are isometric to one of the following manifolds: (i) Sn the standard spher…

We give a full classification of higher order parallel surfaces in three-dimensional homogeneous spaces with four-dimensional isometry group, i.e. in the so-called Bianchi-Cartan-Vranceanu family. This gives a positive answer to a conjecture formulated in 2002. As a partial result, we prove that totally umbilical surfa…

New invariant measures doubly slice links, disproving previous bounds.

Characterizes a specific type of spacetime using vector fields.

It is known that the totally umbilical hypersurfaces in the (n+1)-dimensional spheres are characterized as the only hypersurfaces with weak stability index 0. That is, a compact hypersurface with constant mean curvature, cmc, in S^{n+1}, different from an Euclidean sphere, must have stability index greater than or equa…

Characterizes and examines gradient solitons on doubly warped product manifolds.

Study on CR-lightlike submanifolds in golden semi-Riemannian manifolds.

In \cite{Luo}, the present author proved that if $L$ is a contact stationary Legendrian surface in $\mathbb{S}^5$ with the canonical Sasakian structure and the square length of its second fundamental form belongs to $[0,2]$. Then we have that $L$ is either totally umbilical or is a flat minimal Legendrian torus. In thi…