arXiv research

The object of the present paper is to study locally $φ$-symmetric LP-Sasakian manifolds admitting semi-symmetric metric connection and obtain a necessary and sufficient condition for a locally $φ$-symmetric LP-Sasakian manifold with respect to semi-symmetric metric connection to be locally $φ$-symmetric LP-Sasakian man…

Geodesic completeness proven for all compact locally symmetric Lorentz manifolds.

Defines Jacobi-Koszul-Vinberg structures on Jacobi-left-symmetric algebroids.

Study non-symmetric non-metric connections on Kenmotsu manifolds.

The paper studies quarter-symmetric connections on Hermitian and Kähler manifolds.

Study finds all 4D neutral manifolds.

The paper studies para-Sasaki-like manifolds with a new metric connection.

In this work we prove that every locally symmetric smooth submanifold gives rise to a naturally defined smooth submanifold of the space of symmetric matrices, called spectral manifold, consisting of all matrices whose ordered vector of eigenvalues belongs to the locally symmetric manifold. We also present an explicit f…

Study properties of semi-symmetric Lorentzian spaces, foliated manifolds.

Study constructs Frenet curves using semi-symmetric metric connection.

The paper studies a new connection on Riemannian manifolds and finds conditions for symplectic manifolds.

The study characterizes and verifies equivariant embeddings of symmetric Kählerian manifolds.

The study investigates properties of a specific Riemannian manifold with a semi-symmetric non-metric connection.

The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.

The present study initially identify the generalized symmetric connections of type $(α,β)$, which can be regarded as more generalized forms of quarter and semi-symmetric connections. The quarter and semi-symmetric connections are obtained respectively when $(α,β)=(1,0)$ and $(α,β)=(0,1)$. Taking that into account, a ne…

Geodesic orbit and weakly symmetric properties in spray geometry.

The purpose of the present paper is to study the globally and locally $\varphi$-${\cal T}$-symmetric $\left( \varepsilon \right)$-para Sasakian manifold in dimension $3$. The globally $\varphi$-${\cal T}$-symmetric $3$-dimensional $\left( \varepsilon \right)$-para Sasakian manifold is either Einstein manifold or h…

Lie PCA improves density estimation on symmetric manifolds.

The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric Kenmotsu manifolds with respect to the semi-symmetric non-metric connection.

Study finds lower bounds for energy on fibred manifolds using fiberwise symmetrization.

We classify two-symmetric Lorentzian manifolds using methods of the theory of holonomy groups. These manifolds are exhausted by a special type of pp-waves and, like the symmetric Cahen-Wallach spaces, they have commutative holonomy.

Third-order symmetric Lorentzian manifolds, i.e. Lorentzian manifold with zero third derivative of the curvature tensor, are classified. These manifolds are exhausted by a special type of pp-waves, they generalize Cahen-Wallach spaces and second-order symmetric Lorentzian spaces.

A manifold is locally \emph{$k$-fold symmetric}, if for any point and any $k$-dimensional vector subspace tangent to this point there exists a local isometry such that this point is a fixed point and the differential of the isometry restricted to that $k$-dimensional vector subspace is minus the identity. We show that …

The paper studies $*$-$η$-Ricci-Yamabe solitons on $α$-Cosymplectic manifolds.

Characterizes Lorentzian manifolds with semi-symmetric metric connections.

There is a well developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian manifolds, but some require additional hypotheses. The topics discussed are homogeneity, geodesic completeness, the geodesic orbit…

The paper defines symmetric brackets for skew-symmetric algebroids with totally skew-symmetric torsion.

Hermitian symmetric manifolds are Hermitian manifolds which are homogeneous and such that every point has a symmetry preserving the Hermitian structure. The aim of these notes is to present an introduction to this important class of manifolds, trying to survey the several different perspectives from which Hermitian sym…

Connections with (skew-symmetric) torsion on non-symmetric Riemannian manifold satisfying the Einstein metricity condition (NGT with torsion) are considered. It is shown that an almost Hermitian manifold is an NGT with torsion if and only if it is a Nearly Kähler manifold. In the case of an almost contact metric manifo…

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

Estimates for $p$-capacities on symmetric manifolds.

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

Sharp estimates for parabolic equations on manifolds using symmetrization.

The study realizes symmetric spaces as cotangent bundles and finds nonnegative curvature examples.

A geometry with parallel skew-symmetric torsion is a Riemannian manifold carrying a metric connection with parallel skew-symmetric torsion. Besides the trivial case of the Levi-Civita connection, geometries with non-vanishing parallel skew-symmetric torsion arise naturally in several geometric contexts, e.g. on natural…

The object of the present note is to discuss about the defining condition of weakly cyclic Ricci symmetric manifolds and weakly cyclic $Z$-symmetric manifolds \cite{DMS15} and the existence of such notion by proper examples.

H. A. Hayden [1] introduced the idea of semi-symmetric non-metric connection on a Riemannian manifold in (1932). Agashe and Chafle \cite{1} defined and studied semi-symmetric non-metric connection on a Riemannian manifold. In the present paper, we define a new type of semi-symmetric non-metric connexion in an almost co…

New theorem links quaternionic-Kähler manifolds to symmetric spaces.

Positive simplicial volume implies locally symmetric space structure.

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

Sprays on Frechet manifolds connect connections and tangent structures.

The study examines a semi-symmetric metric connection in perfect fluid space-time and phantom barriers.

The paper geometrizes N-manifolds using symmetric vector bundles.

The paper studies geodesic mappings in special Riemannian manifolds.

We give a complete description of semi-symmetric algebraic curvature tensors on a four-dimensional Lorentzian vector space and we use this description to determine all four-dimensional homogeneous semi-symmetric Lorentzian manifolds.

Study shows lightlike hypersurfaces in indefinite Sasakian manifolds are not symmetric.

Defines semi-symmetric metric connection on super warped products.

In this note we compute low degree rational Pontryagin classes for every closed locally symmetric manifold of noncompact type. In particular, we answer the question: Which locally symmetric M have at least one nonzero Pontryagin class?