arXiv research

Study characterizes 2-Killing vector fields on complex spacetimes.

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…

The paper extends affine connection results to singular warped and twisted products.

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…

For $2+1$ spacetime dimensions, we derive sufficient conditions for the twisting function in a twisted product spacetime, such that there is a global foliation by spacelike CMC surfaces.

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…

Study of spacelike hypersurfaces in twisted product spacetimes with specific conditions.

We consider (flat) Cauchy-complete GH spacetimes, i.e., globally hyperbolic flat lorentzian manifolds admitting some Cauchy hypersurface on which the ambient lorentzian metric restricts as a complete riemannian metric. We define a family of such spacetimes - model spacetimes - including four subfamilies: translation sp…

Study properties of hyperbolic Yamabe solitons in submanifolds.

In this paper, we study Ricci-flat and Einstein Lorentzian multiply warped products. We also consider the case of having constant scalar curvatures for this class of warped products. Finally, after we introduce a new class of spacetimes called as generalized Kasner space-times, we apply our results to this kind of spac…

In this paper, we investigate the null (light-like) sectional curvatures of Lorentzian warped product manifolds. We derive the formulas for the null sectional curvature of many well-known warped product space-time models such as multiply generalized Robertson-Walker space-times, generalized Kasner spacetimes and standa…

Characterizes a specific type of spacetime using vector fields.

Characterizes spacetimes using doubly torqued vectors.

The paper examines conditions for Einstein multiply warped products and estimates their parameters.

In this paper, we define a semi-symmetric metric Killing vector field, then study semi-symmetric metric Killing vector fields on warped and multiply warped products with a semi-symmetric metric connection. We also study Killing and 2-Killing vector fields on multiply warped products.

The paper explores null distance convergence for warped product spacetimes.

Derives formula for present value of future consumer goods multiplier.

Warped-product black hole spacetimes are $C^0$-inextendible.

Spinors prove rigidity for polyhedral spacetime data.

Study on four-dimensional Ricci solitons and multiply warped Ricci flow solutions.

We begin by presenting a symmetric version of the circle equivariant T-duality result in a joint work of the second author with Siye Wu, thereby generalising the results there. We then initiate the study of twisted equivariant Courant algebroids and equivariant generalised geometry and apply it to our context. As befor…

The paper examines gradient ρ-Einstein solitons on specific manifolds and spacetimes.

Formula for index in Lorentzian spacetimes.

Study relationships between intrinsic and extrinsic invariants of Riemannian almost k-product manifolds.

The paper defines and analyzes curvature tensors on super twisted product spaces.

Study a simplified model of multiverse structure with synchronized timelines.

We investigate the geometry of hyperbolic knots and links whose diagrams have a high amount of twisting of multiple strands. We find information on volume and certain isotopy classes of geodesics for the complements of these links, based only on a diagram. The results are obtained by finding geometric information on ge…

Topological twists for 4d N=2 theories depend on spacetime type, gerbe connections, and generalized spin-c structures.

Study proves rigidity of certain gradient steady Ricci solitons with harmonic Weyl curvature.

Given a semi-Riemannian $4$-manifold $(M,g)$ with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of Kähler metrics $g_K$ is constructed, defined on an open set in $M$, which coincides with $M$ in many typical examples. Under certain con…

In the present paper we provide new examples of marginally trapped surfaces and tubes in FLRW spacetimes by using a basic relation between these objects and CMC surfaces in 3-manifolds. We also provide a new method to construct marginally trapped surfaces in closed FLRW spacetimes, which is based on the classical Hopf …

In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular, for two copies of the same group, the twisted product of group by itself throug…

Researchers create spectral triples for twisted crossed products using Kasparov's external product.

Paper studies Landsberg curvature of a specific Finsler metric.

A new algorithm speeds up matrix multiplication without actual multiplication.

On the Geroch-Kronheimer-Penrose future completion $IP(X)$ of a spacetime $X$, there are two frequently used topologies. We systematically examine $τ_+$, the stronger (metrizable) of them, which is the coarsest causally continuous topology, obtaining a variety of novel results, among them a complete characterization of…

On the product of two Finsler manifolds M1 M2, we consider the twisted metric F which is construct by using Finsler metrics F1 and F2 on the manifolds M1 and M2, respectively. We introduce horizontal and vertical distributions on twisted product Finsler manifold and study Creducible and semi-C-reducible properties of t…

Paper studies pseudo-projective tensors on warped products.

Study on balanced Hermitian structures on Lie algebras twisted by representations.

Study constructs non-Riemannian Finsler metrics using warped product.

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…

Some basic geometric properties of doubly twisted product immersions are established.

Rigidity results for hypersurfaces in warped spacetimes.

Given a 3-holed sphere decomposition of an orientable closed surface, it is shown that each orientation preserving homeomorphism of the surface is isotopic to a composition AB where A is a product of positive Dehn twists and B is a product of negative Dehn twists on the decomposition curves.

In this paper, we show that the projection of a dualistic structure defined on a twisted product manifold induces dualistic structures on the base and the fiber manifolds, and conversely. Then under some conditions on the Ricci curvature and the Weyl conformal tensor we characterize dually flat structures on twisted pr…

The Levi-Civita connection and geodesic equations for a stationary spacetime are studied in depth. General formulae which generalize those for warped products are obtained. These results are applicated to some regions of Kerr spacetime previously studied by using variational methods. We show that they are neither space…

We consider knots whose diagrams have a high amount of twisting of multiple strands. By encircling twists on multiple strands with unknotted curves, we obtain a link called a generalized augmented link. Dehn filling this link gives the original knot. We classify those generalized augmented links that are Seifert fibere…

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