arXiv research

The charged Nariai spacetimes are the exact solutions of Einstein-Maxwell field equations with positive cosmological constant and such a spacetime is the direct topological product of a $2$-dimentional de-Sitter spacetime with a round $2$-sphere of constant radius. The present paper deals with the investigation of curv…

The study proves unique static manifolds with positive scalar curvature and boundary.

Study Codazzi tensors in space-times, linking to Cotton gravity.

We give an exhaustive description of bifurcations and of the number of solutions of the vacuum Lichnerowicz equation with positive cosmological constant on $S^1\times S^2$ with $U(1)\times SO(3)$-invariant seed data. The resulting CMC slicings of Schwarzschild-de Sitter and Nariai are described.

We consider static spacetimes whose spatial part admits foliations with the extrinsic curvature tensor K_{ab}=0. There are two complementary cases when the gradient of the lapse function points 1) to the direction of foliation or 2) orthogonally to it. Case 1) gives generalization of metrics like Bertotti-Robinson or N…

As discussed in the paper, in a matter-filled spacetime, perhaps with positive cosmological constant, a stable marginally outer trapped 2-sphere must satisfy a certain area inquality. Namely, its area must be bounded above by $4π/c$, where $c > 0$ is a lower bound on a natural energy momentum term. In this note we cons…

In a matter-filled spacetime, perhaps with positive cosmological constant, a stable marginally outer trapped 2-sphere must satisfy a certain area inequality. Namely, as discussed in the paper, its area must be bounded above by $4π/c$, where $c > 0$ is a lower bound on a natural energy-momentum term. We then consider th…

Study stability and rigidity of axisymmetric marginally outer trapped surfaces.

Uniqueness theorem for extremal charged black holes in de Sitter space.

We consider the vacuum Einstein flow with a positive cosmological constant on spatial manifolds of product form. In spatial dimension at least four we show the existence of continuous families of recollapsing models whenever at least one of the factors or admits a Riemannian Einstein metric with positive Einstein const…

The study proves local rigidity of minimal 2-spheres in electrovacuum spacetimes.

Proves uniqueness of certain spacetime solutions with extremal horizons.

In a recent work, Galloway [9] proved a local foliation theorem by MOTSs for a 3-dimensional initial data set $(M,g,K)$ with mean curvature $τ\le0$ in a 4-dimensional spacetime $(\overline M,\overline g)$ when (under suitable assumptions) $M$ has a stable spherical MOTS $Σ$ which achieves an upper bound for the area. H…

Extends Tian theorem to Vaisman manifolds for approximations.

In 1972, K. Kenmotsu studied a class of almost contact Riemannian manifolds. Later, such a manifold was called a Kenmotsu manifold. This paper, we studied Kenmotsu manifolds with $(2n+s)$-dimensional $s-$contact metric manifold and this manifold, we have called generalized Kenmotsu manifolds. Necessary and sufficient c…

Study on a new type of manifolds that generalize almost C-manifolds.

Stabilized convex symplectic manifolds are equivalent to flexible Weinstein manifolds.

New class of complex manifolds defined, properties studied.

A selfsimiar manifold is a Riemannian manifold $\left(M,g\right)$ endowed with a homothetic vector field $ξ$. We characterize global selfsimilar manifolds and describe the structure of local selfsimilar manifolds. We prove that any selfsimilar manifold with a potential homothetic vector field is a conical Riemannian ma…

Smoothly embed 3-manifolds in 5-manifolds, simplifying topological to smooth.

The study provides a structure theorem for a new class of noncompact 3-manifolds.

Condition for intersection of real flag manifolds in complex flag manifold.

The paper studies extended quasi-Einstein manifolds with special geometric properties and solitons.

Conditions for flat manifolds as cusp cross-sections in arithmetic hyperbolic manifolds.

Classifies 3-manifolds from simplified (2,0)-trisections of 4-manifolds.

Study on 3D manifolds with specific tensor structures and their properties.

New manifold type PNDP-manifold defined with Einstein warped product structure.

Optimal inequalities for systole, inradius, and volume in hyperbolic 3-manifolds

The paper explores F-manifolds and metrics, constructing canonical structures.

Defines s-manifolds and s-manifolds with corners for symplectic applications.

Embeds 3-manifolds in symplectic 4-manifolds with constraints.

We introduce a new general class of metric f-manifolds which we call (nearly) trans-S-manifolds and includes S- manifolds, C-manifolds, s-th Sasakian manifolds and generalized Kenmotsu manifold studied previously. We prove their main properties and we present many examples which justify their study.

The study provides homological characterizations for $Q$-manifolds and $l_2$-manifolds.

A locally conformally Kähler (LCK) manifold $M$ is one which is covered by a Kähler manifold $\tilde M$ with the deck transform group acting conformally on $\tilde M$. If $M$ admits a holomorphic flow, acting on $\tilde M$ conformally, it is called a Vaisman manifold. Neither the class of LCK manifolds nor that of Vais…

Study weak quasi contact metric manifolds to generalize K-contact and Sasakian manifolds criteria.

The study classifies Kähler-Frobenius manifolds and their properties.

Products of LCK manifolds do not admit LCK structures.

Study geodesics on infinite-dimensional manifolds using Finsler structures.

New proof shows compact homogeneous LCK manifolds are Vaisman.

Paper proves existence of minimal surfaces in hyperbolic 3-manifolds.

A universal branched 3-manifold $W$ characterizes Sol 3-manifolds.

The paper proves Liouville theorems for holomorphic maps on pseudo-Hermitian manifolds.

Proves almost flat spin^c manifolds bound compact manifolds.

The paper characterizes graph manifolds using fold maps and embeddability of polyhedra.

The paper defines quasi-isometry for almost contact metric manifolds and explores its properties.

The study identifies flat manifolds with unique cusp cross-sections in arithmetic hyperbolic manifolds.

Study on harmonicity of complex structure on product of trans-Sasakian manifolds.

In this paper, we study the invariant and noninvariant hypersurfaces of (1,1,1) almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an (1,1,1) almost contact manifold admits an almost product structure. We in…