Related papers: Negative Sasakian structures on simply-connected 5…

We prove that any totally geodesic hypersurface $N^5$ of a 6-dimensional nearly K\"ahler manifold $M^6$ is a Sasaki-Einstein manifold, and so it has a hypo structure in the sense of \cite{ConS}. We show that any Sasaki-Einstein 5-manifold…

The present paper deals with some results of submanifolds of generalized Sasakian-space-forms in \cite{ALEGRE3} with respect to semisymmetric metric connection, semisymmetric non-metric connection, Schouten-van Kampen connection and…

We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many distinct tight contact structures within the same homotopy class…

In this paper we have studied pseudosymmetric, Ricci-pseudosymmetric and projectively pseudosymmetric para-Sasakian manifold admitting a quarter-symmetric metric connection and constructed examples of 3-dimensional and 5-dimensional…

Quasi contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of the contact metric manifolds. Weak almost contact metric manifolds, i.e., the linear complex structure on the contact…

We classify fillable contact structures on all negative-definite star-shaped plumbings. Along the way, we show that such Seifert fibred spaces admit a unique negative maximal twisting number, and compute it explicitly using the Alexander…

An important class of contact 3--manifolds are those that arise as links of rational surface singularities with reduced fundamental cycle. We explicitly describe symplectic caps (concave fillings) of such contact 3--manifolds. As an…

We classify the resolution graphs of weighted homogeneous surface singularities which admit rational homology disk smoothings. The nonexistence of rational homology disk smoothings is shown by symplectic geometric methods, while the…

We show that a statistical manifold manifold of a constant non-zero curvature can be realised as a level line of Hessian potential on a Hessian cone. We construct a Sasakian structure on $TM\times\R$ by a statistical manifold manifold of a…

We study positive definite quaternionic contact $(4n+3)$-manifolds ($qc$-manifold for short). Just like the $CR$-structure contains the class of Sasaki manifolds, the $qc$-structure admits a class of $3$-Sasaki manifolds with integrable…

First, we prove that indefinite Sasakian manifolds do not admit any screen conformal $r$-null submanifolds, tangent to the structure vector field. We, therefore, define a special class of null submanifolds, called; {\it contact screen…

We study the question of existence of a Riemannian metric of positive scalar curvature metric on manifolds with the Sullivan-Baas singularities. The manifolds we consider are Spin and simply connected. We prove an analogue of the…

The aim of this paper is to study Sasakian immersions of compact Sasakian manifolds into the odd-dimensional sphere equipped with the standard Sasakian structure. We obtain a complete classification of such manifolds in the Einstein and…

Special-generic-like maps or SGL maps are introduced by the author motivated by observing and investigating algebraic topological or differential topological properties of manifolds via nice smooth maps whose codimensions are negative. The…

We show that if $N$ is a closed manifold of dimension $n=4$ (resp. $n=5$) with $\pi_2(N) = 0$ (resp. $\pi_2(N)=\pi_3(N)=0$) that admits a metric of positive scalar curvature, then a finite cover $\hat N$ of $N$ is homotopy equivalent to…

We enumerate all possible types of spacetime causal structures that can appear in static, spherically symmetric configurations of a self-gravitating, real, nonlinear, minimally coupled scalar field \phi in general relativity, with an…

This paper provides a topological method for filling contact structures on the connected sums of $S^2\times S^3$. Examples of nonsymplectomorphic strong fillings of homotopy equivalent contact structures with vanishing first Chern class on…

In the literature, there are two different versions of Hard Lefschetz theorems for a compact Sasakian manifold. The first version, due to Kacimi-Alaoui, asserts that the basic cohomology of a compact Sasakian manifold satisfies the…

In this short note we present some remarks concerning anti-quasi-Sasakian manifolds. Some proofs of their basic properties are simplified. We also discuss some canonical invariant distributions which exist on every anti-quasi-Sasakian…

Is any positive knot the closure of a positive braid? No. But if we consider positivity in terms of the generators of the braid group due to Birman, Ko and Lee, then the answer is yes. In this paper we prove that the same occurs when…