arXiv research

Study the geometry of transversal lightlike submanifolds in Metallic Semi-Riemannian manifolds.

Study on lightlike hypersurfaces in metallic semi-Riemannian manifolds.

Study on lightlike submanifolds in metallic semi-Riemannian manifolds.

Study characterizes submanifolds in metallic semi-Riemannian manifolds with specific connections.

Characterizes metallic structures on product manifolds and provides conditions for warped products to be metallic.

The paper characterizes metallic pseudo-Riemannian manifolds using conjugate connections and tensor structures.

Harmonic metallic structures on compact manifolds are equivalent to vanishing of their metallic structure.

The paper explores metallic structures on manifolds using a special ratio.

Study properties of hemi-slant submanifolds in metallic Riemannian manifolds.

Study properties of metallic Riemannian submanifolds.

The study explores properties of slant and semi-slant submanifolds in metallic Riemannian manifolds.

Study on submanifolds in metallic Riemannian manifolds.

In this paper, we introduce metallic maps between metallic Riemannian manifolds, provide an example and obtain certain conditions for such maps to be totally geodesic. We also give a sufficient condition for a map between metallic Riemannian manifolds to be harmonic map. Then we investigate the constancy of certain map…

Study metallic structures on P-Sasakian manifolds.

Study metallic Riemannian structures on submanifolds of Riemannian manifolds.

Review of metallic Riemannian geometry advances.

Study properties of specific submanifolds in metallic Riemannian spaces.

We consider submanifolds into Riemannian manifold with metallic structures. We obtain some new results for hypersurfaces in these spaces and we express the fundamental theorem of submanifolds into products spaces in terms of metallic structures. Moreover, we define new structures called complex metallic structures. We …

Definition of $({\cal T}_{a},{\cal T}_{b})$-pseudosymmetric semi-Riemannian manifold is given. $({\cal T}_{a},{\cal T}_{b})$-pseudosy mmetric $(N(k),ξ)$-semi-Riemannian manifolds are classified. Some results for ${\cal T}_{a}$-pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifolds are obtained. $({\cal T}_{a},{\cal T}_{b…

$(N(k),ξ)$-semi-Riemannian manifolds are defined. Examples and properties of $(N(k),ξ)$-semi-Riemannian manifolds are given. Some relations involving ${\cal T}_{a}$-curvature tensor in $(N(k),ξ)$-semi-Riemannian manifolds are proved. $ξ$-${\cal T}_{a}$-flat $(N(k),ξ)$-semi-Riemannian manifolds are defined. It is proved…

Study on CR-lightlike submanifolds in golden semi-Riemannian manifolds.

Study the geometry of specific submanifolds in Golden Semi-Riemannian manifolds.

The paper studies lightlike submanifolds in bronze semi-Riemannian manifolds with specific geometric properties.

We classify semi-Riemannian submersions with connected totally geodesic fibres from a real pseudo-hyperbolic space onto a semi-Riemannian manifold under the assumption that the dimension of the fibres is less than or equal to three and the metrics induced on fibres are negative definite. Also, we obtain the classificat…

Study on null helices in semi-Riemannian manifolds with special submanifolds.

This thesis extends noncommutative geometry to semi-Riemannian manifolds and applies it to gauge theories.

In this paper we study a semi-Riemannian submersion from Lorentzian (para)almost contact manifolds and find necessary and sufficient conditions for the characteristic vector field to be vertical or horizontal. We also obtain decomposition theorems for an anti-invariant semi-Riemannian submersion from Lorentzian (para)S…

The paper proves weak continuity of Cartan structural system on semi-Riemannian manifolds with lower regularity.

The paper explores polyharmonic curves in semi-Riemannian manifolds.

Using screen distributions and lightlike transversal vector bundles we develop a theory of degenerate foliations of semi-Riemannian manifolds.

The existence of closed hypersurfaces of prescribed curvature in semi-riemannian manifolds is proved provided there are barriers.

Study of null hypersurfaces in semi-Riemannian manifolds with applications.

We show that every analytic semi-Riemannian manifold can be isometrically embeddded into an Einstein maifold in co-dimension one.

Conditions for metallic structures to induce integrable distributions and geodesic invariance.

The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian case correspond to one-sided bounds on the sectional curvatures. Starting from 2-d…

We find the index of $\widetilde{\nabla}$-quasi-conformally symmetric and $\widetilde{\nabla}$-concircularly symmetric semi-Riemannian manifolds, where $\widetilde{\nabla}$ is metric connection.

This paper presents an investigation of the relation between some positivity of the curvature and the finiteness of fundamental groups in semi-Riemannian geometry. We consider semi-Riemannian submersions $π: (E, g) \rightarrow (B, -g_{B})$ under the condition with $(B, g_{B})$ Riemannian, the fiber closed Riemannian, …

We classify the semi-Riemannian submersions from a pseudo-hyperbolic space onto a Riemannian manifold under the assumption that the fibres are connected and totally geodesic. Also we obtain the classification of the semi-Riemannian submersions from a complex pseudo-hyperbolic space onto a Riemannian manifold under the …

In the present article the geometry of semi-Riemannian manifolds with nonholonomic constraints is studied. These manifolds can be considered as analogues to the sub-Riemannian manifolds, where the positively definite metric is substituted by a nondegenerate metric. To study properties of the exponential map the Christo…

Study metallic structures on tangent bundles with lifts and integrability.

We prove the semi-Riemannian bumpy metric theorem using equivariant variational genericity. The theorem states that, on a given compact manifold $M$, the set of semi-Riemannian metrics that admit only nondegenerate closed geodesics is generic relatively to the $C^k$-topology, $k=2,...,\infty$, in the set of metrics of …

Study lightlike submanifolds in Golden Semi-Riemannian geometry.

The study extends Hano's theorem to semi-Riemannian product manifolds with specific conditions.

Study metallic structures on generalized tangent bundles.

In this article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Rie…

On a Riemannian or a semi-Riemannian manifold, the metric determines invariants like the Levi-Civita connection and the Riemann curvature. If the metric becomes degenerate (as in singular semi-Riemannian geometry), these constructions no longer work, because they are based on the inverse of the metric, and on related o…

In this paper we introduce paraquaternionic CR-submanifolds of almost paraquaternionic hermitian manifolds and state some basic results on their differential geometry. We also study a class of semi-Riemannian submersions from paraquaternionic CR-submanifolds of paraquaternionic Kaehler manifolds.

New types of semi-Riemannian manifolds with linear curvature conditions identified.