arXiv research

This article is a continuation of my former article "On Connectivity Spaces". After some brief historical references relating to the subject, separation spaces and then adjoint notions of connective representation and connective foliation are developed. The connectivity order previously defined only in the finite case …

New $\mathcal{C}$-connection characterizes 4D spaces conformal to Einstein spaces.

Study on Einstein warped spaces with specific connections and curvature properties.

Characterizes group connections on group bundles.

Defines semi-symmetric metric connection on super warped products.

The paper defines Dirac structures on connection spaces and their properties.

Study classifies Einstein-Yang-Mills spaces in 4D symmetric spaces.

The kth finite subset space of a topological space X is the space exp_k X of non-empty subsets of X of size at most k, topologised as a quotient of X^k. Using results from our earlier paper (math.GT/0210315) on the finite subset spaces of connected graphs we show that the kth finite subset space of a connected cell com…

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

Study projective connections on surfaces using osculating spaces.

Study of minimal surfaces in 3D space with special connections.

We consider local invariants of general connections (with torsion). The group of origin-preserving diffeomorphisms acts on a space of jets of general connections. Dimensions of moduli spaces of generic connections are calculated. Poincaré series of the geometric structure of connection is constructed, and shown to be a…

The action of origin-preserving diffeomorphisms on a space of jets of symmetric connections is considered. Dimensions of moduli spaces of generic connections are calculated. Poincaré series of the geometric structure of symmetric connection is constructed, and shown to be a rational function.

The paper characterizes surfaces in 4D space forms with flat normal connection.

Study on HYM connections on Kähler manifolds, calculating moduli space virtual dimension.

Study Hom-Lie algebroid connections on complex manifolds.

Study information geometry of warped product spaces, finding special connections.

Study classifies moduli spaces of spin connections on 3D homogeneous spaces.

We study Yang-Mills connections on holomorphic bundles over complex Kähler manifolds of arbitrary dimension, in the spirit of Hitchin's and Simpson's study of flat connections. The space of non-Hermitian Yang-Mills (NHYM) connections has dimension twice the space of Hermitian Yang-Mills connections, and is locally isom…

The present paper deals with some results of submanifolds of generalized Sasakian-space-forms in \cite{ALEGRE3} with respect to semisymmetric metric connection, semisymmetric non-metric connection, Schouten-van Kampen connection and Tanaka-webster connection.

Research shows RCD* spaces are semi-locally simply connected.

In this paper, we study CAT(0) spaces with non-locally connected boundary. We give some condition of a CAT(0) space whose boundary is not locally connected.

Reinterprets Schrödinger equation using Cartan connection for geometric investigation.

In this paper we construct a Hitchin connection in a setting, which significantly generalizes the setting covered by the first author previously, which in turn was a generalisation of the moduli space case covered by Hitchin in his original work on the Hitchin connection. In fact, our construction provides a Hitchin co…

Genus 3 Heegaard groups of lens space connected sums are finitely generated.

Instantons on ALF spaces constructed from bow data.

For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear connections that can be associated with a system of SODE and a generalized Lagrange struc…

In this paper, we describe the space of adapted connections on a metric contact manifold through the space of their torsion tensors. The torsion tensor is an element of the space of TM-valued two-forms, which splits into various subspaces. We study the parts of the torsion tensor according to this splitting to complete…

We attach copies of the circle to points of a countable dense subset $D$ of a separable metric space $X$ and construct an earring space $E(X,D)$. We show that the fundamental group of $E(X,D)$ is isomorphic to a subgroup of the Hawaiian earring group, if the space $X$ is simply-connected and locally simply-connected. I…

We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere, a compact Lie group with a bi-invariant metric or its symmetric dual. In partic…

Study biharmonic hypersurfaces in Sasakian space form using Tanaka-Webster connection.

Quantum connections replace metrics with operator inner products.

Study invariant connections on multivariate Gaussian distributions.

We introduce a symplectic structure on the space of connections in a G-principal bundle over a four-manifold and the Hamiltonian action on it of the group of gauge transformations which are trivial on the boundary. The symplectic reduction becomes the moduli space of flat connections over the manifold. On the moduli sp…

Classifies 3D spaces using specific invariants.

Study special affine connections on symmetric spaces and their products.

We show that if a Finsler space is conformally automorphic to a Riemannian space and the automorphism is positively homogeneous with respect to tangent vectors, then the indicatrix of the Finsler space is a space of constant curvature. In this case, the Finslerian two-vector angle can explicitly be found, which gives r…

No exceptional orbits found in Hilbert spaces actions.

Connected space of Dirac-minimal metrics in 2 and 4 dimensions.

SU(2) flat connection on 2D Riemann surface is shown to relate to the generalized twisted geometry in 3D space with cosmological constant. Various flat connection quantities on Riemann surface are mapped to the geometrical quantities in discrete 3D space. We propose that the moduli space of SU(2) flat connections on Ri…

Ricci limit spaces are semi-locally simply connected.

Symmetric spaces' connections form Lie admissible triple algebras.

The paper explores symplectic connections on homogeneous spaces, finding a unique invariant connection.

This paper explores Lorentzian manifolds with specific connections and their symmetries.

This paper is devoted to a systematic study and classification of invariant affine or metric connections on certain classes of naturally reductive spaces. For any non-symmetric, effective, strongly isotropy irreducible homogeneous Riemannian manifold $(M=G/K, g)$, we compute the dimensions of the spaces of $G$-invarian…

We determine loop space decompositions of simply-connected four-manifolds, $(n-1)$-connected $2n$-dimensional manifolds provided $n\notin\{4,8\}$, and connected sums of products of two spheres. These are obtained as special cases of a more general loop space decomposition of certain torsion-free $CW$-complexes with wel…

Simply connected spaces of tight frames identified.

Deform moment map on symplectic connections using star product algebras.