arXiv research

The paper establishes new Casorati inequalities for various Riemannian maps and submersions.

Study on Riemannian Poisson warped product spaces and their properties.

Paper studies quaternionic space forms and Riemannian maps inequalities.

The paper classifies submanifolds in pseudo-Riemannian space forms.

Researchers provide explicit parametrizations for Sasakian space forms.

Survey on smooth function and form density in Riemannian Sobolev spaces.

The paper derives inequalities for Riemannian submersions and their applications.

The paper derives curvature inequalities for submersions from quaternionic space forms.

Paper establishes new inequality for Riemannian maps and applies it to various space forms.

The paper derives Chen-Ricci inequalities for Riemannian submersions and maps.

The paper derives inequalities for Riemannian submersions and applies them to specific space forms.

The paper classifies PMCV hypersurfaces in non-flat pseudo-Riemannian space forms.

Establish generalized Chen inequalities for Riemannian submersions and Riemannian maps with applications.

The paper derives optimal inequalities for bi-slant submanifolds in metallic Riemannian space forms.

The paper derives inequalities for Riemannian maps and submersions involving quaternionic space forms.

Completes the space of vector-valued one-forms on manifolds.

We obtain sharp inequalities involving the Ricci curvature and the scalar curvature for anti-invariant Riemannian submersions from Sasakian space forms onto Riemannian manifolds.

New quasi space forms solve Thurston's geometrical space form problem.

The paper sets new bounds for Ricci-curvature in submersions and maps.

We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannia…

Study on a specific type of Riemannian manifolds constructed from 2D space-forms.

The paper proves a new inequality for submanifolds in Riemannian space forms and applies it to find minimal submanifolds.

The Pontryagin forms on 1-jet bundle of Riemannian metrics, are shown to provide, in a natural way, diffeomorphism-invariant pre-symplectic structures on the space of Riemannian metrics for dimensions $n=4r-2$. The equivariant Pontryagin forms provide canonical moment maps for these structures. In dimension two, the sy…

Geodesic orbit spaces and their families are studied in pseudo-Riemannian manifolds.

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

In this paper, we derived biharmonic equations for pseudo-Riemannian submanifolds of pseudo-Riemannian manifolds which includes the biharmonic equations for submanifolds of Riemannian manifolds as a special case. As applications, we proved that a pseudo-umbilical biharmonic pseudo-Riemannian submanifold of a pseudo-Rie…

Extends cohomology to incomplete Riemannian manifolds.

Study curvature operator on Riemannian manifolds, proving new classification results.

The paper classifies and explores isoparametric hypersurfaces in pseudo-Riemannian space forms.

Killing forms on Riemannian manifolds are differential forms whose covariant derivative is totally skew--symmetric. We show that a compact simply connected symmetric space carries a non--parallel Killing $p$--form ($p\ge2$) if and only if it isometric to a Riemannian product $S^k\times N$, where $S^k$ is a round sphere…

Study immersions of surfaces into SL(2,C) and geodesics space.

Computes tube formulas for valuations in complex space forms.

Paper proves inequalities for forms on sub-Riemannian manifolds.

The paper proves existence and uniqueness of slant immersions in complex space forms.

Researchers generalize space forms in Riemannian geometry using specific vector fields.

The theory of harmonic symmetric bilinear forms on a Riemannian manifold is an analogue of the theory of harmonic exterior differential forms on this manifold. To show this, we must consider every symmetric bilinear form on a Riemannian manifold as a one-form with values in the cotangent bundle of this manifold. In thi…

In this paper, we study biconservative hypersurfaces in $\mathbb S^{n}$ and $\mathbb H^{n}$. Further, we obtain complete explicit classification of biconservative hypersurfaces in $4$-dimensional Riemannian space form with exactly three distinct principal curvatures.

The paper studies biharmonic conformal hypersurfaces in Riemannian manifolds.

In this paper, we consider surfaces in 4--dimensional pseudo--Riemannian space--forms with index 2. First, we obtain some of geometrical properties of such surfaces considering their relative null space. Then, we get classifications of quasi--minimal surfaces with positive relative nullity.

We classify the space-like biharmonic surfaces in 3-dimension pseudo-Riemannian space form, and construct explicit examples of proper biharmonic hypersurfaces in general ADS space.

The paper studies $f$-biharmonic maps and submersions in space forms.

We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences between global isometric immersion problems among different space forms …

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denot…

Classifies 4D spaces with compact Clifford-Klein forms.

The paper explores polyharmonic hypersurfaces in pseudo-Riemannian space forms.

We study left-invariant Killing $k$-forms on simply connected $2$-step nilpotent Lie groups endowed with a left-invariant Riemannian metric. For $k=2,3$, we show that every left-invariant Killing $k$-form is a sum of Killing forms on the factors of the de Rham decomposition. Moreover, on each irreducible factor, non-ze…

The paper constructs all cmc hypersurfaces with two principal curvatures.

Let $M$ be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces $H^p$ of differential forms on $M$ and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the $H^p$-boundedness for Riesz transforms on $M$, g…