arXiv research

Inverse mean curvature flows studied in warped product manifolds with positive warping factor.

The study examines scalar curvature in direct product Riemannian manifolds and their multiconformal classes.

We study warped compactifications of string/M theory with the help of effective potentials, continuing previous work of the last two authors and Michael R. Douglas presented in arXiv:1206.1885. The dynamics of the conformal factor of the internal metric, which is responsible for instabilities in these constructions, is…

The paper studies affine connections on singular warped products and their curvature.

Study on submanifolds with specific types of factors in Kaehler manifolds.

Essentially, some conditions for the Riemannian factor and the warping function of a standard static space-time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space-time Einstein.

The paper confirms a conjecture about manifolds with positive curvature.

Characterizes and examines gradient solitons on doubly warped product manifolds.

New rigidity found for 3D warped product domains.

Let $[γ]$ be the conformal boundary of a warped product $C^{3,α}$ AHE metric $g=g_M+u^2h$ on $N=M \times F$, where $(F,h)$ is compact with unit volume and nonpositive curvature. We show that if $[γ]$ has positive Yamabe constant, then $u$ has a positive lower bound that depends only on $[γ]$.

The purpose of this article is to study implications of a Ricci soliton warped product manifold to its base and fiber manifolds. First, it is proved that if a warped product manifold is Ricci soliton then its factors are Ricci soliton. Then we study Ricci soliton on warped product manifolds admitting either a conformal…

Painlevé analysis identifies integrable cases of Ricci solitons over specific warped products and line bundles.

Study optimal inequality for contact CR-warped product submanifolds in cosymplectic space forms.

Unified positive mass theorem and Dirac operator study on weighted manifolds.

We derive one unified formula for Ricci curvature tensor on arbitrary warped product manifold by introducing a new notation for the lift vector and the Levi-Civita connection.This formula is helpful to further consider Ricci flow (RF) and hyperbolic geometric flow (HGF) and evolution equations on warped product manifol…

Study on new warped product submanifolds in para-Kähler manifolds.

Study properties of hyperbolic Yamabe solitons in submanifolds.

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

Study on rigidity of warped cones and expanders.

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

Study of IMCF on warped product manifolds for long time existence.

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, …

The paper explores Einstein warped G2 and Spin(7) manifolds.

In this paper we show that an expanding or steady gradient Ricci soliton warped product $B^n\times_f F^m$, $m>1$, whose warping function $f$ reaches both maximum and minimum must be a Riemannian product. Moreover, we present a necessary and sufficient condition for constructing a gradient Ricci soliton warped product. …

The article surveys recent results on warped and CR-warped product submanifolds in Kaehler manifolds.

The paper proves rigidity for submanifolds in warped product manifolds.

Proves conjecture for symmetric manifolds with positive scalar curvature.

We study pseudo-Riemannian Einstein manifolds which are conformally equivalent with a metric product of two pseudo-Riemannian manifolds. Particularly interesting is the case where one of these manifolds is 1-dimensional and the case where the conformal factor depends on both manifolds simultaneously. If both factors ar…

Rigidity results for hypersurfaces in warped spacetimes.

The study introduces a new curvature concept for weighted graphs and applies it to warped products.

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Rie…

The paper examines conditions for Einstein-like classes in doubly warped product manifolds.

The paper estimates heights of H-surfaces in warped products with conditions.

The study constructs gradient Einstein-type warped metrics and proves nonexistence and rigidity results.

Study new types of submanifolds in Kenmotsu manifolds.

In this paper we apply the anholonomic frames method developed in refs. [1-4] to construct and study anisotropic vacuum field configurations in 5D gravity. Starting with an off--diagonal 5D metric, parameterized in terms of several ansatz functions, we show that using anholonomic frames greatly simplifies the resulting…

The paper proves rigidity for warped product spaces with degenerate ends.

Warped product construction for Finsler manifolds with curvature conditions.

The warped product $N_1\times_f N_2$ of two Riemannian manifolds $(N_1,g_1)$ and $(N_2,g_2)$ is the product manifold $N_1\times N_2$ equipped with the warped product metric $g=g_1+f^2 g_2$, where $f$ is a positive function on $N_1$. The notion of warped product manifolds is one of the most fruitful generalizations of R…

Compact fibration metrics inherit positive holomorphic curvature.

Researchers solve a Riemannian geometry problem using warped products.

Study on special symmetries in biwarped product 3-manifolds.

Study shows nonextendibility of warped spacelike singularities in specific spacetimes.

Study biharmonic submanifolds in warped product structures.

Study finds curvature estimates for starshaped hypersurfaces in warped product manifolds.

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 $I$.

New metrics on 3D manifolds with large Steklov eigenvalues.

In the framework of Lorentzian warped products, we study the Friedmann-Robertson-Walker cosmological model to investigate non-smooth curvatures associated with multiple discontinuities involved in the evolution of the universe. In particular we analyze non-smooth features of the spatially flat Friedmann-Robertson-Walke…