Related papers: Three-dimensional almost Kenmotsu manifolds satisf…

A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e., these structures…

The Kakimizu complex is usually defined in the context of knots, where it is known to be quasi-Euclidean. We here generalize the definition of the Kakimizu complex to surfaces and 3-manifolds (with or without boundary). Interestingly, in…

The Newman-Penrose-Perjes formalism is applied to smooth contact structures on riemannian 3-manifolds. In particular it is shown that a contact 3-manifold admits an adapted riemannian metric if and only if it admits a metric with a…

In this short note, as a simple application of the strong result proved recently by B\"ohm and Wilking, we give a classification on closed manifolds with 2-nonnegative curvature operator. Moreover, by the new invariant cone constructions of…

An \emph{$\omega$-admissible almost complex structure} on a $2n$-dimensional symplectic manifold $(M,\omega)$ is a $\omega$-calibrated almost complex structure $J$ admitting a nowhere vanishing $\bar{\partial}_J$-closed $(n,0)$-form $\psi$.…

The object of the present paper is to characterize two classes of almost Kenmotsu manifolds admitting Ricci-Yamabe soliton. It is shown that a $(k,\mu)'$-almost Kenmotsu manifold admitting a Ricci-Yamabe soliton or gradient Ricci-Yamabe…

We find necessary and sufficient conditions for a complete $n$-dimensional Riemannian manifold of finite volume, whose curvature tensor has nullity at least $n-2$, to be a geometric graph manifold. In the process, we show that Nomizu's…

In this paper we construct and study almost paracontact metric structures $(\varphi ,\xi ,\eta ,g)$ on a 3-dimensional Walker manifold $(M,g)$ with respect to a local basis only by the coordinate functions of a unit space-like vector field…

Motivated by cosmic censorship in general relativity and string theory, we extend Christodoulou's celebrated examples of naked singularity formation in the Einstein-massless scalar field system to include a positive or negative scalar…

In this article, we first show that given a smooth function $ S $ either on closed manifolds $ (M, g) $ or compact manifolds $ (\bar{M}, g) $ with non-empty boundary, both for dimensions at least $ 3 $, the condition $ S \equiv 0 $, or $ S…

We propose the study of some kind of monopole equations directly associated with a contact structure. Through a rudimentary analysis about the solutions, we show that a closed contact 3-manifold with positive Tanaka-Webster curvature and…

We characterize quasi K\"ahler manifolds whose curvature tensor associated to the canonical Hermitian connection satisfies the first Bianchi identity. This condition is related with the third Gray identity and in the almost K\"ahler case…

In the Cauchy problem for asymptotically flat vacuum data the solution-jets along the cylinder at space-like infinity develop in general logarithmic singularities at the critical sets at which the cylinder touches future/past null infinity.…

We prove (Theorem 1.1.) that a class of quasi-Einstein structures on closed manifolds must admit a Killing vector field. This extends the rigidity theorem obtained in \cite{DL23} for the extremal black hole horizons and completes the…

In this paper, we consider $*$-Ricci soliton in the frame-work of Kenmotsu manifolds. First, we prove that if the metric of a Kenmotsu manifold $M$ is a $*$-Ricci soliton, then soliton constant $\lambda$ is zero. For 3-dimensional case, if…

We define the notion of an exceptional manifold to be a flat Riemannian manifold with boundary which supports a positive harmonic function satisfying simultaneously a zero Dirichlet condition and a constant (nonzero) Neumann condtion at the…

In the present paper, we characterize almost Kenmotsu manifolds admitting holomorphically planar conformal vector (HPCV) fields. We have shown that if an almost Kenmotsu manifold $M^{2n+1}$ admits a non-zero HPCV field $V$ such that $\phi V…

We prove that a compact, connected, and oriented 4-dimensional gradient $m$-quasi-Einstein manifold with $m\in [1, \infty]$ which is additionally a spin manifold must satisfy the Hitchin-Thorpe Inequality. We show further that the…

In this article we introduce $A$-valued Einstein-Hilbert-Palatini functional ($A$-EHP) over a n-manifold $M$, where $A$ is an arbitrary graded algebra, as a generalization of the functional arising in the study of the first order…

We investigate curvature properties of 3-$(\alpha,\delta)$-Sasaki manifolds, a special class of almost 3-contact metric manifolds generalizing 3-Sasaki manifolds (corresponding to $\alpha = \delta = 1$) that admit a canonical metric…