arXiv research

Study on Riemannian Poisson warped product spaces and their properties.

Linear classifiers in product space forms improve scRNA-seq data classification.

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

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

Classifies hypersurfaces with constant curvature in product spaces.

We give a complete classification of submanifolds with parallel second fundamental form of a product of two space forms. We also reduce the classification of umbilical submanifolds with dimension $m\geq 3$ of a product $\Q_{k_1}^{n_1}\times \Q_{k_2}^{n_2}$ of two space forms whose curvatures satisfy $k_1+k_2\neq 0$ to …

The paper calculates curvatures in a specific type of warped product space.

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

This article begins the theory of submanifolds into products of 2 or more space forms. The tensors $\mathbf{R}$, $\mathbf{S}$ and $\mathbf{T}$ defined by Lira, Tojeiro and Vitório at \cite{LTV} and the Bonnet theorem proved by them are generalized for the product of many space forms. Besides, some examples given by Men…

We obtain a basic inequality involving the Laplacian of the warping function and the squared mean curvature of any warped product isometrically immersed in a Riemannian manifold without assuming any restriction on the Riemann curvature tensor of the ambient manifold. Applying this general theory, we obtain basic inequa…

Study classifies Einstein spaces and warped products in weighted geometry.

In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold. Moreover, we obtain some geometric inequalities for C-totally real doubly warped product submanifolds of generaliz…

B.-Y. Chen initiated the study of warped product submanifolds in his fundamental seminal papers \cite{C1,C2,C2.1}. In this paper, we study contact CR-warped product submanifolds of cosymplectic space forms and prove an optimal inequality by using Gauss and Codazzi equations. In addition, we obtain two geometric inequal…

We give a complete classification of umbilical surfaces of arbitrary codimension of a product $Q^{n_1}_{k_1}\times Q^{n_2}_{k_2}$ of space forms whose curvatures satisfy $k_1 + k_2 \not= 0$.

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

We translate into the double forms formalism the basic identities of Greub and Greub-Vanstone that were obtained in the mixed exterior algebra. In particular, we introduce a second product in the space of double forms, namely the composition product, which provides this space with a second associative algebra structure…

We give local, explicit representation formulas for n-dimensional spacelike submanifolds which are marginally trapped in the Minkowski space, the de Sitter and anti de Sitter spaces and the Lorentzian products of the sphere and the hyperbolic space by the real line.

Study minimal Kähler submanifolds in product of space forms.

The paper proves a new inequality for CR-warped product submanifolds in complex space forms.

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

The paper studies Steklov eigenvalues in space forms and warped product manifolds, deriving bounds and monotonicity results.

We provide a local classification of isometric immersions $f\colon L^p\times_ρM^n\to\Q_c^{p+n+k}$ in codimensions $k=1, 2$ of warped products of Riemannian manifolds into space forms, under the assumptions that $n\geq k+1$ and that $N^{p+n}=L^p\times_ρM^n$ has no points with the same constant sectional curvature $c$ as…

We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally decomposed as a product manifold endowed with a polar metric. For a product manifold endowed with a polar metric, our …

We provide conditions under which an isometric immersion of a (warped) product of manifolds into a space form must be a (warped) product of isometric immersions.

The paper classifies isoparametric hypersurfaces in product spaces with different curvatures.

n this paper, we obtain a geometric inequality between the length of the second fundamental form and the length of Lee form in terms of the warping function for a CR-warped product submanifold in a locally conformal Kaehler space form. The equality case is also investigated. Furthermore, the inequality is discussed for…

Currents on Lie groups form a Hopf algebra structure.

Estimates mean curvature, scalar curvature, shape operator in warped products.

The paper examines stability of Minkowski inequalities in warped product spaces.

In this paper we consider minimal Lagrangian submanifolds in $n$-dimensional complex space forms. More precisely, we study such submanifolds which, endowed with the induced metrics, write as a Riemannian product of two Riemannian manifolds, each having constant sectional curvature. As the main result, we give a complet…

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…

Study on instantons over product manifolds with a codimension-4 form.

The paper derives inequalities for contact CR-warped product submanifolds in cosymplectic space forms.

The study extends $L^p$-spectrum analysis to warped products and Kleinian groups.

We consider surfaces with parallel mean curvature vector (pmc surfaces) in $\mathbb{C}P^n\times\mathbb{R}$ and $\mathbb{C}H^n\times\mathbb{R}$, and, more generally, in cosymplectic space forms. We introduce a holomorphic quadratic differential on such surfaces. This is then used in order to show that the anti-invariant…

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

In this paper we introduce a local approach for the study of maximal surfaces immersed into a Lorentzian product space of the form $M^2\times R_1$, where $M^2$ is a connected Riemannian surface and $M^2\times R_1$ is endowed with the product Lorentzian metric. Specifically, we establish a local integral inequality for …

The product of smooth valuations on manifolds is described in terms of differential forms, Gelfand transforms and blow-up spaces. It is shown that the product extends partially to generalized valuations and corresponds geometrically to transversal intersections. This result is used to prove a general kinematic formula …

The study examines hypersurfaces in warped products and their properties.

Formula for spacelike submanifolds in warped products.

Recently, M. Atcken studied Contact CR-warped prod- uct submanifolds in cosymplectic space forms and established gen- eral sharp inequalities for CR-warped products in a cosymplectic manifold [1]. In the present paper, we obtain an inequality for the squared norm of the second fundamental form in terms of constant ?$φ$…

In this paper, we discuss the Weyl problem in warped product space. We obtain the openness, non rigidity and some applications. These results together with the a priori estimates obtained by Lu imply some existence results. Meanwhile we reprove the infinitesimal rigidity in the space forms.

We prove a homological stability theorem for moduli spaces of high-dimensional, highly connected manifolds, with respect to forming the connected sum with the product of spheres $S^{p}\times S^{q}$, for $p < q < 2p - 2$. This result is analogous to recent results of S. Galatius and O. Randal-Williams regarding the homo…

Geometrically, tensors of fixed rank form a minimal submanifold.

We prove a Simons type formula for submanifolds with parallel mean curvature vector field in product spaces of type $M^n(c)\times\mathbb{R}$, where $M^n(c)$ is a space form with constant sectional curvature $c$, and then we use it to characterize some of these submanifolds.

The paper classifies λ-biharmonic hypersurfaces in product spaces.

Quasi-isometries in horospherical products are close to product maps.

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…