arXiv research

Study shape operator of relatively parallel hypersurfaces in n-dimensional geometry.

The paper proves Bonnet-type theorems for hypersurfaces in 4D space.

Study of convex hypersurfaces with specific curvature properties.

The paper classifies hypersurfaces with parallel almost paracontact structures.

In this paper we deal with relative normalizations of hypersurfaces in the (n+1)-dimensional Euclidean space $\mathbb{R}^{n+1}$. Considering a relative normalization $\bar{y}$ of an hypersurface $Φ$ we decompose the corresponding Tchebychev vector $\bar{T}$ in two components, one parallel to the Tchebychev vector $\bar…

The paper examines conditions of parallelism for a special tensor on 3D hypersurfaces.

Classifies and describes hypersurfaces in Siklos spacetimes.

Study classifies hypersurfaces with parallel structure Jacobi operator in complex quadric.

Study of spacelike submanifolds with umbilical lightlike normals in Lorentzian spacetimes.

Complete classification of centroaffine hypersurfaces with parallel cubic form.

Classifies Calabi hypersurfaces with parallel Fubini-Pick form.

Classifies special hypersurfaces in Gödel spacetimes.

Classifies special hypersurfaces in specific types of manifolds.

Paper proves non-existence of certain hypersurfaces in complex quadric.

Study classifies real hypersurfaces with special Jacobi operator in complex hyperbolic quadric.

The study finds necessary and sufficient conditions for $C^1$-hypersurfaces to have nowhere $C^1$-regular parallel sets.

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

No real hypersurfaces found in complex Grassmannians with specific Jacobi operators.

Mean curvature flow by parallel hypersurfaces is solved for isoparametric hypersurfaces.

Paper studies second order symmetric parallel tensors in generalized f.pk-space forms.

Paper classifies special Euclidean hypersurfaces with specific geometric properties.

The study characterizes canal hypersurfaces formed by non-null curves with parallel frame in Minkowski space-time.

There are several kinds of classification problems for real hypersurfaces in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$. Among them, Suh classified Hopf hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$ with Reeb parallel Ricci tensor in Levi-Civita connection. In this paper, we introduce a new notion of gene…

This paper classifies hypersurfaces in n+1 with parallel Fubini-Pick form.

We prove that there does not exist any semi-parallel real hypersurface in complex two-plane Grassmannians. With this result, the nonexistence of recurrent real hypersurfaces in complex two-plane Grassmannians can also be proved.

We study three dimensional real hypersurfaces in CP^2 and CH^2 equipped with $xi$-parallel structure Jacobi operator. We prove that they are Hopf hypersurfaces and if additional $α\neq0$, we classify them.

We classify real hypersurfaces in CP^2and CH^2 equipped with pseudo-parallel structure Jacobi operator.

Study proves no lightlike hypersurfaces exist in certain indefinite Sasakian manifolds.

The paper classifies real hypersurfaces with a special structure in complex quadrics.

The objective of the present paper is to prove the non-existence of real hypersurface with pseudo-parallel normal Jacobi operator in complex two-plane Grassmannians. As a corollary, we show that there does not exist any real hypersurface with semi-parallel or recurrent normal Jacobi operator in complex two-plane Grassm…

Formula for spacelike submanifolds in warped products.

We prove the non-existence of real hypersurfaces in CP^2 and CH^2 whose structure Jacobi operator is Lie D-parallel.

In 1970, Samuel I. Goldberg and Kentaro Yano defined the notion of noninvariant hypersurface of a Sasakian manifold [1]. In this paper we have studied the properties of parallel vector fields with respect to induced connection on the noninvariant hypersurface $M$ of a Sasakian manifold $\tilde M$ with $(φ, g, u, v, λ)-…

Study on relative entropy for hypersurfaces in hyperbolic space.

The paper characterizes hypersurfaces in curved spaces using their geometry.

The paper examines stable CMC hypersurfaces with boundaries on parallel hyperplanes.

In this paper, we introduce new notions of semi-parallel shape operators and structure Jacobi operators in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$. By using such a semi-parallel condition, we give a complete classification of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$.

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

In this paper, we give a complete conformal classification of the regular space-like hypersurfaces in the de Sitter Space $\mathbb{S}^{m+1}_{1}$ with parallel para-Blaschke tensors.

The non-existence of three dimensional real hypersurfaces in non-flat complex space forms with parallel *-Ricci tensor is proved.At the end of the papaer ideas for further research on *-Ricci tensor are provided.

The paper studies inverse mean curvature flow on hypersurfaces in space forms.

We consider non-degenerate centro-affine hypersurface immersions in R^n whose cubic form is parallel with respect to the Levi-Civita connection of the affine metric. There exists a bijective correspondence between homothetic families of proper affine hyperspheres with center in the origin and with parallel cubic form, …

Two Spin^c structures characterize hypersurfaces in product spaces.

The paper studies $f$-stability of hypersurfaces in gradient Ricci solitons.

Study of superintegrable systems linked to affine hypersurfaces.

The paper defines and studies equiaffine isoparametric hypersurfaces and functions.

In this paper, we use two conformal non-homogeneous coordinate systems, modeled on the de Sitter space ${\mathbb S}^{m+1}_1$, to cover the conformal space ${\mathbb Q}^{m+1}_1$, so that the conformal geometry of regular space-like hypersurfaces in $\mathbb{Q}^{m+1}_1$ is treated as that of hypersurfaces in ${\mathbb S}…

The study classifies special Lorentz surfaces in a 4-space with neutral metric.