arXiv research

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

Constructs local superconformal algebras on supermanifolds.

Defines semi-symmetric metric connection on super warped products.

The paper studies special warped products with a specific connection on super Riemannian manifolds.

We conjecture formulae of the colored superpolynomials for a class of twist knots $K_p$ where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomial for the twist k…

With the usual definition of a super Hilbert space and a super unitary representation, it is easy to show that there are lots of super Lie groups for which the left-regular representation is not super unitary. I will argue that weakening the definition of a super Hilbert space (by allowing the super scalar product to b…

The object of the present paper is to obtain the characterization of a warped product semi-Riemannian manifold with a special type of recurrent like structure, called super generalized recurrent. As consequence of this result we also find out the necessary and sufficient conditions for a warped product manifold to sati…

Modernizes higher-dimensional supergravity, linking it to flux quantization.

On a five dimensional simply connected Sasaki-Einstein manifold, one can construct Yang-Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however the contact instanton equations are not elliptic. It turns out that these equa…

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

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.

We use invariance theory to compute the divergence term $a_{m+2,m}^{d+δ}$ in the super trace for the twisted de Rham complex for a closed Riemannian manifold.

In this paper we construct an explicit representative for the Grothendieck fundamental class [Z] of a complex submanifold Z of a complex manifold X, under the assumption that Z is the zero locus of a real analytic section of a holomorphic vector bundle E. To this data we associate a super-connection A on the exterior a…

Paper studies Landsberg curvature of a specific Finsler metric.

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…

A key open problem in M-theory is the mechanism of "gauge enhancement", which supposedly makes M-branes exhibit the nonabelian gauge degrees of freedom that are seen perturbatively in the limit of 10d string theory. In fact, since only the twisted K-theory classes represented by nonabelian Chan-Paton gauge fields on D-…

In these lectures we review how the symmetries of gravitational theories may be regarded as originating from those of "Yang-Mills squared". We begin by motivating the idea that certain aspects of gravitational theories can be captured by the product, in some sense, of two distinct Yang-Mills theories, particularly in t…

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…

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

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.

Study characterizes 2-Killing vector fields on complex 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.

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 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…

Matrix formulas for super Teichmüller spaces generalize previous work and yield super λ-lengths.

Dirac-harmonic maps are uncoupled under certain conditions.

The Legendrian product of two Legendrian knots, as defined by Lambert-Cole, is a Legendrian torus. We show that this Legendrian torus is a twist spun whenever one of the Legendrian knot components is sufficiently large. We then study examples of Legendrian products which are not Legendrian isotopic to twist spuns. In o…

This paper computes fixed point Floer cohomology for Dehn twists on surfaces.

In this paper we present a certain class of geodesic vector fields of the double-twisted product R X R. Some examples of totally geodesic foliations are given.

We show that the chiral de Rham complex of a generalized Calabi-Yau manifold carries N=2 supersymmetry. We discuss the corresponding topological twist for this N=2 algebra. We interpret this as an algebroid version of the super-Sugawara or Kac-Todorov construction.

Extends Wigner's representation to study super hyperbolic geometry.

In the present paper we prove Liouville-type theorems: non-existence theorems for complete twisted and warped products of Riemannian manifolds which generalize and complement similar results for compact manifolds.

The paper proves a theorem for a twisted Dirac operator on specific manifolds.

This paper explores twisted Lagrangian tori in C^2 and their Hamiltonian stationarity.

Algorithm detects free products in disk mapping class groups.

New rigidity results for warped product domains.

New method for pricing financial products without no-arbitrage condition.

Smooth superspace with special weights has a Fubini-Study form.

The paper proves a theorem for a twisted Dirac operator on specific manifolds.

New relation found in 4D symplectic mapping class group.

Friedl and Kim show any taut sutured manifold can be realized as a twisted homology product, but their proof gives no practical description of how complicated the realizing representation needs to be. We give a number of results illustrating the relationship between the topology of a taut sutured handlebody and the com…

We propose a model in which a spliced vector bundle (with an arbitrary number of gauge structures in the splice) possesses a geometry which do not split. The model employs connection 1-forms with values in a space-product of Lie algebras, and therefore interlaces the various gauge structures in a non-trivial manner. Sp…

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

We provide an upper bound on the topological complexity of twisted products. We use it to give an estimate $TC(X)\le TC(π_1(X))+\dim X$ of the topological complexity of a space in terms of its dimension and the complexity of its fundamental group.

A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a meromorphic map. These conformal maps adopt properties of a holomorphic function or a me…

Develops a theorem for a 6D manifold with boundary.