arXiv research

I discuss geometry and normal forms for pseudo-Riemannian metrics with parallel spinor fields in some interesting dimensions. I also discuss the interaction of these conditions for parallel spinor fields with the condition that the Ricci tensor vanish (which, for pseudo-Riemannian manifolds, is not an automatic consequ…

We present some results on the boundedness of the mean curvature of proper biharmonic submanifolds in spheres. A partial classification result for proper biharmonic submanifolds with parallel mean curvature vector field in spheres is obtained. Then, we completely classify the proper biharmonic submanifolds in spheres w…

Study proves 3-manifolds with parallel vector fields have odd Betti numbers.

Study surfaces with parallel mean curvature in 4D spaces.

On a Lorentzian manifold the existence of a parallel null vector field implies certain constraint conditions on the induced Riemannian geometry of a space-like hypersurface. We will derive these constraint conditions and, conversely, show that every real analytic Riemannian manifold satisfying the constraint conditions…

We construct a special class of Lorentz surfaces in the pseudo-Euclidean 4-space with neutral metric which are one-parameter systems of meridians of rotational hypersurfaces with timelike or spacelike axis and call them meridian surfaces. We give the complete classification of the meridian surfaces with parallel mean c…

Geometrically describes surfaces with parallel mean curvature in warped product spaces.

The paper examines parallel one forms on Riemannian and Finslerian manifolds.

Study on generalized ξ-parallel maps in Riemannian geometry.

The spinor flow stability is proven for Ricci flat metrics and parallel spinor fields.

In 1970, Samuel I. Goldberg and Kentaro Yano defined the notion of noninvariant hypersurface of a Sasakian manifold [1]. In this paper we have studied the properties of parallel vector fields with respect to induced connection on the noninvariant hypersurface $M$ of a Sasakian manifold $\tilde M$ with $(φ, g, u, v, λ)-…

We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for graphs of bounded degree, its complexity is linear in the number of cliques. Unlike…

Paper studies second order symmetric parallel tensors in generalized f.pk-space forms.

We obtain several rigidity results for biharmonic submanifolds in $\mathbb{S}^{n}$ with parallel normalized mean curvature vector field. We classify biharmonic submanifolds in $\mathbb{S}^{n}$ with parallel normalized mean curvature vector field and with at most two distinct principal curvatures. In particular, we dete…

The paper classifies hypersurfaces with parallel almost paracontact structures.

In this paper we proof that the Holomorphic angle for compact minimal surfaces in the sphere $S^5$ with constant Contact angle and with a parallel normal vector field must be constant.

The paper examines soliton surfaces using a parallel transport frame field in 4D space.

Geodesic completeness and flow properties of compact Brinkmann spacetimes proven.

Einstein's philosophy uses differential identities to derive GR field equations.

New inequality shows all special submanifolds in light cone are totally umbilical spheres.

We show that for $n>2$ a compact locally conformally Kähler manifold $(M^{2n},g,J)$ carrying a non-trivial parallel vector field is either Vaisman, or globally conformally Kähler, determined in an explicit way by some compact Kähler manifold of dimension $2n-2$.

Study timelike surfaces with parallel mean curvature in Minkowski 4-space.

We classify complete biharmonic surfaces with parallel mean curvature vector field and non-negative Gaussian curvature in complex space forms.

The study classifies special Lorentz surfaces in a 4-space with neutral metric.

We describe the compact Lorentzian $3$-manifolds admitting a parallel lightlike vector field. The classification of compact Lorentzian $3$-manifolds admitting non-isometric affine diffeomorphisms follows, together with the complete description of these morphisms. Such a Lorentzian manifold is in some sense an equivaria…

Study infinitesimal deformations of Killing spinors on nearly parallel G2-manifolds.

New method finds vector fields with maximal Jacobi operator rank in manifolds.

New approach to nematic fields on surfaces, relaxing uniformity to quasi-uniformity.

Unified description of string and brane worldvolumes using auto-parallel vector fields.

A new algorithm speeds up solving complex spin system problems.

Theory of parallel transport on non-collapsed RCD spaces established.

A submanifold of a pseudo-Riemannian manifold is said to have parallel mean curvature vector if the mean curvature vector field H is parallel as a section of the normal bundle. Submanifolds with parallel mean curvature vector are important since they are critical points of some natural functionals. In this paper, we su…

Mathematical theory of super fiber bundles and connections developed.

Study timelike meridian surfaces in Minkowski 4-space with specific properties.

Study of $η$-Ricci solitons on $(\varepsilon)$-almost paracontact metric manifolds.

Using the theory of extensors developed in a previous paper we present a theory of the parallelism structure on arbitrary smooth manifold. Two kinds of Cartan connection operators are introduced and both appear in intrinsic versions (i.e., frame independent) of the first and second Cartan structure equations. Also, the…

Study parallel tensors on affine surfaces to characterize Ricci recurrence.

It is proved the non-existence of Hopf hypersurfaces in $G_{2}({\Bbb C}^{m+2})$, $m \geq 3$, whose normal Jacobi operator is semi-parallel, if the principal curvature of the Reeb vector field is non-vanishing and the component of the Reeb vector field in the maximal quaternionic subbundle ${\frak D}$ or its orthogonal …

New findings on Codazzi tensors in homogeneous spaces.

The bienergy of a vector field on a Riemannian manifold (M,g) is defined to be the bienergy of the corresponding map (M,g) ---> (TM,g_S), where the tangent bundle TM is equipped with the Sasaki metric g_S. The constrained variational problem is studied, where variations are confined to vector fields, and the correspond…

We provide explicit spinor representations for Clifford algebras.

The study classifies parallel mean curvature spheres in a sphere-hyperbolic product space.

Any Spin(7)-manifold admits a metric connection \nabla^c with totally skew-symmetric torsion T^c preserving the underlying structure. We classify those with \nabla^c-parallel T^c\neq0 and non-Abelian isotropy algebra iso(T^c)<spin(7). These are isometric to either Riemannian products or homogeneous naturally reductive …

The paper studies Einstein-like Walker metrics in Walker manifolds.

This work proposes an efficient autoregressive model for text generation.

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold $(M,g)$ is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of $(M,g)$. We characterize the following simply connected pseudo-Riemannian manifolds admitting such subbundles in terms of their…

We classify 7-dimensional cocalibrated $\G_2$-manifolds with parallel characteristic torsion and non-abelian holonomy. All these spaces admit a metric connection $\nabla^{\mathrm{c}}$ with totally skew-symmetric torsion and a spinor field $Ψ_1$ solving the equations in the common sector of type II superstring theory. T…

Study finds holonomy algebras for Lorentzian Weyl spin manifolds with specific spinors.