arXiv research

The paper examines biconservative hypersurfaces with constant curvature in space forms.

Study classifies 3D self-shrinkers with constant second form norm.

Classifies hypersurfaces with constant curvature in product spaces.

New findings on hypersurfaces with specific curvature properties in space forms.

The paper classifies and constructs rotational surfaces with constant astigmatism in space forms.

2-stein submanifolds in space forms have constant curvature if normal connection is flat or codimension is 2.

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

Classifies hypersurfaces with constant isotropic curvature in space forms.

Paper proves biharmonic hypersurfaces in nonzero space form have constant mean curvature.

Geodesic spheres are the only quasicomplete surfaces in 3-space-forms.

Study on biconservative hypersurfaces with constant scalar curvature in space forms.

Hypersurfaces with constant Ricci eigenvalues in real space forms are classified.

Complete classification of isoparametric hypersurfaces in product spaces of space forms.

The paper classifies surfaces with constant skew curvature in 3-space forms.

The paper studies stable surfaces with constant curvature in 3D space forms.

New gap theorem for hypersurfaces with constant mean curvature in space forms.

Paper classifies special slant surfaces with varying curvature.

Sasakian immersions prove Sasaki-Ricci solitons are η-Einstein with rational constants.

Study Hamiltonian stationary Lagrangian surfaces in complex space forms.

Researchers classify 3D self-shrinkers in 4D space.

The paper improves proximity estimates for hypersurfaces with almost constant curvature in space forms.

Minimal hypersurfaces are the only $H$-tensional in 4D space forms.

In this paper, we show that a generalized Sasakian space form of dimension greater than three is either of constant sectional curvature; or a canal hypersurface in Euclidean or Minkowski spaces; or locally a certain type of twisted product of a real line and a flat almost Hermitian manifold; or locally a wapred product…

The study defines and constructs hypersurfaces in a product of two space forms.

Study ruled real hypersurfaces in nonflat complex space forms with constant norm shape operators.

Classifies weakly Einstein hypersurfaces in spaces of constant curvature.

The paper classifies product minimal Lagrangian submanifolds in complex space forms.

The following theorem is proved: If an AH3-manifold M of dimension greather or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then M is a real space form or a complex space form.

The complete local classification and geometric description of n-dimensional submanifolds F with recurrent nonparallel second fundamental form in the spaces of constant curvature M(c) are obtained in this article.

The paper examines 4D hypersurfaces with constant mean curvature in pseudo-Riemannian space forms.

Study on polyharmonic curves on spheres and space forms.

The study proves conditions for constant curvature submanifolds in space forms.

We give some classifications of biharmonic hypersurfaces with constant scalar curvature. These include biharmonic Einstein hypersurfaces in space forms, compact biharmonic hypersurfaces with constant scalar curvature in a sphere, and some complete biharmonic hypersurfaces of constant scalar curvature in space forms and…

The study classifies and constructs examples of surfaces with specific curvature and boundary conditions.

Let $M^n$ be a biharmonic hypersurface with constant scalar curvature in a space form $\mathbb M^{n+1}(c)$. We show that $M^n$ has constant mean curvature if $c>0$ and $M^n$ is minimal if $c\leq0$, provided that the number of distinct principal curvatures is no more than 6. This partially confirms Chen's conjecture and…

Study proves radial symmetry of solutions to certain nonlinear equations in space forms.

Let $M$ be a compact $n$-manifold of $\operatorname{Ric}_M\ge (n-1)H$ ($H$ is a constant). We are concerned with the following space form rigidity: $M$ is isometric to a space form of constant curvature $H$ under either of the following conditions: (i) There is $ρ>0$ such that for any $x\in M$, the open $ρ$-ball at $x^…

In this paper we study the behavior of the scalar curvature $S$ of a complete hypersurface immersed with constant mean curvature into a Riemannian space form of constant curvature, deriving a sharp estimate for the infimum of $S$. Our results will be an application of a weak Omori-Yau maximum principle due to Pigola, R…

We derive some elliptic differential inequalities from the Weitzenböck formulas for the traceless Ricci tensor of a Kähler manifold with constant scalar curvature and the Bochner tensor of a Kähler-Einstein manifold respectively. Using elliptic estimates and maximum principle, some $L^p$ and $L^\infty$ pinching result…

Kähler-Ricci solitons can be immersed into complex space forms if and only if the manifold is Einstein.

The study classifies isoparametric hypersurfaces in product spaces with constant angle function.

A new method is presented for solving the Gauss-Codazzi equations for a compact Riemann surface to be immersed in a 3-manifold of constant curvature. In the negative curvature case, the moduli for such embeddings are cohomology classes of (0,2) forms.

The paper proves curvature inequalities for submanifolds in space forms.

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…

The study constructs pressure form on Margulis spacetimes and proves their infinitesimal rigidity.

We show that there is no phi-recurrent generalized Sasakian-space-forms, when is a non-zero constant.

The paper finds formulas for special surface shapes in 3D space.

Researchers classify special curved spheres in a complex space.