Recent Advances in Riemannian and Lorentzian Geometries

@inproceedings{Duggal2003RecentAI,
  title={Recent Advances in Riemannian and Lorentzian Geometries},
  author={Krishan L. Duggal and Ramesh Sharma},
  year={2003}
}

Some Inequalities on Half Lightlike Submanifolds of a Lorentzian Manifold with Semi-Symmetric Metric Connection

  • N. PoyrazBurçin Doḡan
  • Mathematics
    NATURENGS MTU Journal of Engineering and Natural Sciences Malatya Turgut Ozal University
  • 2021
In this paper, we introduce some inequalities for screen homothetic half lightlike submanifolds of a real space form of constant sectional curvature , endowed with semi-symmetric metric connection.

A Study on Chen-like Inequalities for Half Lightlike Submanifolds of a Lorentzian Manifold Endowed with Semi-Symmetric Metric Connection

  • N. PoyrazBurçin Doḡan
  • Mathematics
    NATURENGS MTU Journal of Engineering and Natural Sciences, Malatya Turgut Ozal University
  • 2020
In this paper, Chen-like inequalities of a half lightlike submanifolds of a real space form N(c) with constant sectional curvature c, equipped with semi-symmetric metric connection are established

On a deformed Riemannian extension of affine Szabó connections

In this paper, we exhibit example of Szabó metrics of neutral signature, which is obtained by the deformed Riemannian extension. M.S.C. 2010: 53B05; 53B20; 53C50.

k-Plane Constant Curvature Conditions

This research generalizes the two invariants known as constant sectional curvature (csc) and constant vector curvature (cvc). We use k-plane scalar curvature to investigate the higher-dimensional

Some Inequalities for Ricci Solitons

where LVg is a Lie-derivative of the metric tensor g with respect to V , Ric is the Ricci tensor of (M, g), λ is a constant and X,Y are arbitrary vector fields on M. Hence the Ricci soliton denotes

Putting the “ k ” in Curvature: k -Plane Constant Curvature Conditions

This research generalizes the properties known as constant sectional curvature and constant vector curvature in Riemannian model spaces of arbitrary finite dimension. While these properties have been

Ideality of a Coisotropic Lightlike Submanifold

The notion of best living way on coisotropic lightlike submanifolds is discussed. Some relations involving the screen Ricci curvature and the screen scalar curvature are given. Two examples of

Affine Szab\'o connections on smooth manifolds

In this paper, we introduce a new structure, namely, affine Szab\'o connection. We prove that, on $2$-dimensional affine manifolds, the affine Szab\'o structure is equivalent to one of the cyclic

On three dimensional affine Szabó manifolds

In this paper, we consider the cyclic parallel Ricci tensor condition, which is a necessary condition for an affine manifold to be Szab\'o. We show that, in dimension $3$, there are affine manifolds

The 1965 Penrose singularity theorem

We review the first modern singularity theorem, published by Penrose in 1965. This is the first genuine post-Einsteinian result in general relativity, where the fundamental and fruitful concept of

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