arXiv research

The study compares and finds Yamabe constants on warped products.

No conformal product structures on compact manifolds with constant curvature.

Classifies hypersurfaces with constant curvature in product spaces.

Study on warped product Yamabe solitons with constant fiber curvature.

The paper classifies hypersurfaces in $\mathbb{H}^2 imes\mathbb{H}^2$ with constant curvature.

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

This paper mixes constant sum and constant product market makers to improve their features.

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

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

The paper derives height estimates for surfaces with constant curvature in warped product spaces.

The paper classifies various types of hypersurfaces in a product space.

The paper proves rigidity for hypersurfaces with constant shifted curvature functions in warped product manifolds.

Paper analyzes constant-product market making protocols.

Study on hypersurfaces in pseudo-Euclidean space with constant curvature or rotational properties.

Proves rigidity of boundaries with constant mean curvature in warped product manifolds.

The study classifies isoparametric and homogeneous hypersurfaces in product spaces.

Let (V,g) and (W,h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V x W, g+h) in terms of the conformal Yamabe constants of (V,g) and (W,h).

The paper modifies a warped product space to find conditions for constant height functions.

The paper classifies hypersurfaces in a product of two spheres with constant curvature.

The paper classifies λ-biharmonic hypersurfaces in product spaces.

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

Characterizes warping functions in Einstein Poisson warped spaces.

The study classifies isoparametric hypersurfaces in specific product spaces.

The paper studies properties of intrinsically Lipschitz constants in metric spaces.

Study proves rigidity for Heintze-Karcher inequality in substatic manifolds.

The paper classifies hypersurfaces in Riemannian manifolds with constant inner product and torse-forming axes.

The special nature of gradient Yamabe soliton equation which was first observed by Cao-Sun-Zhang\cite{CaoSunZhang} shows that a complete gradient Yamabe soliton with non-constant potential function is either defined on the Euclidean space with rotational symmetry, or on the warped product of the real line with a manifo…

In this paper we characterize compact and complete hypersurfaces with some constant higher order mean curvature into warped product spaces. Our approach is based on the use of a new trace operator version of the Omori-Yau maximum principle which seems to be interesting in its own.

In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connecti…

In this paper, we first investigate several rigidity problems for hypersurfaces in the warped product manifolds with constant linear combinations of higher order mean curvatures as well as "weighted'' mean curvatures, which extend the work \cite{Mon, Brendle,BE} considering constant mean curvature functions. Secondly, …

Let $I \subseteq \R$ be an open interval, $f : I \to \R$ a strictly positive function and denote by $\E^2$ the Euclidean plane. We classify all surfaces in the warped product manifold $I \times_f \E^2$ for which the unit normal makes a constant angle with the direction tangent to $I$.

For a closed Riemannian manifold $(M^m,g)$ of constant positive scalar curvature and any other closed Riemannian manifold $(N^n,h)$, we show that the limit of the Yamabe constants of the Riemannian products $(M\times N,g+rh)$ as $r$ goes to infinity is equal to the Yamabe constant of $(M^m \times R^n, [g+g_E])$ and is …

In the first part of this paper we outline the constructions and properties of Fedosov star product and Berezin-Toeplitz star product. In the second part we outline the basic ideas and recent developments on Yau-Tian-Donaldson conjecture on the existence of Kähler metrics of constant scalar curvature. In the third part…

In this paper, we compute the index form of the multiply twisted products. We study the Killing vector fields on the multiply twisted product manifolds and determine the Killing vector fields in some cases. We compute the curvature of the multiply twisted products with a semi-symmetric metric connection and show that t…

We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped product type. Our main result is an upper bound on the resonance counting function with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base manifold defining the ends.

In this paper we obtain a sharp height estimate concerning compact hypersurfaces immersed into warped product spaces with some constant higher order mean curvature, and whose boundary is contained into a slice. We apply these results to draw topological conclusions at the end of the paper.

Survey on conjugate surfaces in product spaces.

Study biharmonic curves in warped product manifolds with curvature analysis.

The paper solves a specific Dirichlet problem for constant mean curvature surfaces in a particular manifold.

We consider the conformal class of the Riemannian product $g_0 + g$, where $g_0$ is the constant curvature metric on $S^m$ and $g$ is a metric of constant scalar curvature on some closed manifold. We show that the number of metrics of constant scalar curvature in the conformal class grows at least linearly with respect…

We consider surfaces with constant mean curvature in certain warped product manifolds. We show that any such surface is umbilic, provided that the warping factor satisfies certain structure conditions. This theorem can be viewed as a generalization of the classical Alexandrov theorem in Euclidean space. In particular, …

In this paper, we study the Einstein warped products and multiply warped products with a quarter-symmetric connection. We also study warped products and multiply warped products with a quarter-symmetric connection with constant scalar curvature. Then apply our results to generalized Robertson-Walker spacetimes with a q…

Given a warped product of the real line with a Riemannian manifold of arbitrary dimension, we classify the hypersurfaces whose tangent spaces make a constant angle with the vector field tangent to the real direction. We show that this is a natural setting in which to extend previous results in this direction made by se…

We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds which can be written as a twisted product are those of constant curvature…

Let $(M^m,g_M)$ be a closed, connected manifold with positive scalar curvature and $(T^k,g)$ some flat $k$-Torus of unit volume. By a result of F. Dobarro and E. Lami Dozo, there exists a unique $f: M \rightarrow \mathbf{R}_{>0}$ such that the warped product $M\times_f T^k$ has constant scalar curvature and unit volume…

In this paper we show that a compact warped product Einstein manifold with vanishing Bach tensor of dimension $n \geq 4$ is a finite quotient of a warped product with $(n-1)$-dimensional Einstein fiber. The fiber has constant curvature if $n=4$.

The paper studies Einstein hypersurfaces in a specific warped product space.

Topological theory for qLDPC codes enables non-Clifford gates and magic state injection.