arXiv research

The study characterizes spacetimes with quasi-constant sectional curvature and explores their properties in $\mathcal{F}(\mathcal{R})$-gravity.

The aim of this paper is to classify compact Kahler manifolds with quasi-constant holomorphic sectional curvature.

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizi…

We prove that closed manifolds admitting a generic metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC spaces where sets of isotropic points are arbitrary, under suitable positivity assumption and for torsion-free fundamental groups they are still diff…

Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal sectional curvatures are locally equivalent to canal hypersurfaces in Euclidean spa…

In this paper, we show that a generalized Sasakian space form of dimension greater than three is either of constant sectional curvature; or a canal hypersurface in Euclidean or Minkowski spaces; or locally a certain type of twisted product of a real line and a flat almost Hermitian manifold; or locally a wapred product…

We prove that every Kaehler metric, whose potential is a function of the time-like distance in the flat Kaehler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local classification of the Kaehler manifolds with the above mentioned metrics. New examples o…

The paper describes a specific type of Kähler surfaces.

Using as an underlying manifold an alpha-Sasakian manifold we introduce warped product Kaehler manifolds. We prove that if the underlying manifold is an alpha-Sasakian space form, then the corresponding Kaehler manifold is of quasi-constant holomorphic sectional curvatures with special distribution. Conversely, we prov…

The aim of this paper is to describe Kahler surfaces with quasi-constant holomorphic curvature

The Eisenhart problem of finding parallel tensors treated already in the framework of quasi-constant curvature manifolds in \cite{x:j} is reconsidered for the symmetric case and the result is interpreted in terms of Ricci solitons. If the generator of the manifold provides a Ricci soliton then this is i) expanding on p…

Study on generalized quasi-Einstein structures in contact geometry.

Extended recurrent pseudo-Riemannian manifolds were introduced by Mileva Prvanovic'. We reconsider her work in the light of recent results and show that the manifold is conformally flat, and it is a space of quasi-constant curvature. We also show that an extended recurrent Lorentzian manifold, with time-like associated…

The paper introduces comprehensive quasi-Einstein spacetimes and explores their properties.

The study improves Wintgen inequalities for submanifolds in specific geometric spaces.

Study finds conditions for certain warped product manifolds to be quasi-Einstein.

We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the curve graphs and the mapping class groups.

The Chern sectional curvature of a Hermitian manifold is derived and related to Kähler metrics.

New proof shows holomorphic sectional curvature fully determines curvature tensor.

The paper extends a theorem about Kähler manifolds with quasi-negative curvature to almost quasi-negative curvature.

We prove that a product complex manifold cannot admit a complete Kähler metric with sectional curvature $K<c<0$ and Ricci curvature $Ric > d$, where $c$ and $d$ are constants. In particular, a product domain in $\C$ cannot cover a compact Kähler manifold with negative sectional curvature. On the other hand, we observe …

The paper proves that Kähler manifolds with positive holomorphic sectional curvature have a limited diameter.

We prove the following results: An almost Hermitian manifold of indefinite metric is of pointwise constant holomorphic sectional curvature if the holomorphic sectional curvature is bounded from above and from below. If the antiholomorphic sectional curvature is bounded either from above or from below, then the manifold…

We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal Kähler manifold with constant nonpositive holomorphic sectional curvature is Kähler. We also give examples of complete non-Kähler metrics with pointwise negative c…

It is proved that if an AK2-manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then it is a 6-dimensional manifold of constant negative sectional curvature or a Kähler manifold of constant holomorphic sectional curvature.

Formula for sectional curvatures on matrix groups.

Formula for sectional curvature on 2D Lorentzian manifolds derived.

The φ-sectional curvature of statistical structures on almost contact metric manifolds is always non-positive.

4-manifolds with nonnegative sectional curvature are area-extremal.

The paper extends Gray's result to quaternion-Kähler manifolds.

In this paper, we obtain classification of four-dimensional Einstein manifolds with positive Ricci curvature and pinched sectional curvature. In particular, the first result concerns with an upper bound of sectional curvature, improving a theorem of E. Costa. The second is a generalization of D. Yang's result assuming …

Curvature flows in hyperbolic space preserve positive sectional curvature and contract to a point.

The paper proves properties of complex manifolds with nonnegative holomorphic sectional curvature.

New theorem links quaternionic-Kähler manifolds to symmetric spaces.

Let M be an almost Hermitian manifold of dimension greater or equal to 6. The following theorems are proved: Theorem 1. If M is of pointwise constant θ-holomorphic sectional curvature for a number θ in (0,π/2) then M is of constant sectional curvature or a Kähler manifold of constant holomorphic sectional curvature. Th…

In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.

Directly proves Wu's theorem on negative curvature metrics.

Ricci flow preserves positive sectional curvature on homogeneous spheres

No conformal product structures on compact manifolds with constant curvature.

In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field. We give several simple examples of Riemannian metrics which do not have positive sectional curvature but support a vector field…

We algebraically compute all possible sectional curvature values for canonical algebraic curvature tensors, and use this result to give a method for constructing general sectional curvature bounds. We use a well-known method to geometrically realize these results to produce a hypersurface with prescribed sectional curv…

Nonnegative sectional curvature linked to matrix displacement convexity.

Extends Eells-Sampson theorem for manifolds with positive sectional curvature bounds.

Classifies Kähler metrics with constant holomorphic curvature.

In [11], I. M. Gelfand, V. Retakh, and M. Shubin defined the symplectic sectional curvature of a torsion-free connection preserving a symplectic form. The present article defines the corresponding notion of constant symplectic sectional curvature and characterizes this notion in terms of the curvature tensor of the sym…

Every biharmonic Wintgen ideal submanifold in a Riemannian manifold of constant sectional curvature is either minimal or has constant mean curvature.

Upper bound found for dimensions of subspaces where holomorphic sectional curvature vanishes.

New curvature obstruction for Killing vector fields on Lorentzian manifolds.