Related papers: A Bonnet-Myers type theorem for quaternionic conta…

By a theorem of Banyaga the group of diffeomorphisms of a manifold $P$ preserving a regular contact form $\alpha$ is a central $S^1$ extension of the commutator of the group of symplectomorphisms of the base $B = P/S^1$. We show that if $T$…

The paper describes relations between Liouville type theorems for solutions of a periodic elliptic equation (or a system) on an abelian cover of a compact Riemannian manifold and the structure of the dispersion relation for this equation at…

On a Riemannian manifold of dimension $n$ we extend the known analytic results on Yang-Mills connections to the class of connections called $\Omega$-Yang-Mills connections, where $\Omega$ is a smooth, not necessarily closed, $(n-4)$-form.…

We show that, under a certain condition, contact 5-manifolds can `coarsely' distinguish smooth structures on compact Stein 4-manifolds via contact open books. We also give a simple sufficient condition for an infinite family of Stein…

In this paper, we first prove the $f$-mean curvature comparison in a smooth metric measure space when the Bakry-Emery Ricci tensor is bounded from below and $|f|$ is bounded. Based on this, we define a Myers-type compactness theorem by…

A contact projective structure is a contact path geometry the paths of which are among the geodesics of some affine connection. In the manner of T.Y. Thomas there is associated to each contact projective structure an ambient affine…

Almost contact manifolds with B-metric are considered. A special linear connection is introduced, which preserves the almost contact B-metric structure on these manifolds. This connection is investigated on some classes of the considered…

We prove a Steiner formula for regular surfaces with no characteristic points in 3D contact sub-Riemannian manifolds endowed with an arbitrary smooth volume. The formula we obtain, which is equivalent to a half-tube formula, is of local…

In this paper, we prove that a compact quasi-Einstein manifold $(M^n,\,g,\,u)$ of dimension $n\geq 4$ with boundary $\partial M,$ nonnegative sectional curvature and zero radial Weyl tensor is either isometric, up to scaling, to the…

After observing that the well-known convexity theorems of symplectic geometry also hold for compact contact manifolds with an effective action of a torus whose Reeb vector field corresponds to an element of the Lie algebra of the torus, we…

The famous Hopf-Rinow Theorem states, amongst others, that a Riemannian manifold is metrically complete if and only if it is geodesically complete. The Clifton-Pohl torus fails to be geodesically complete proving that this theorem cannot be…

The regularity of limit spaces of Riemannian manifolds with L^p curvature bounds, $p > n/2$, is investigated under no apriori non-collapsing assumption. A regular subset, defined by a local volume growth condition for a limit measure, is…

We establish curvature obstruction theorems for manifolds with boundary. Our main theorems show that, for dimensions up to 7, a topologically nontrivial compact manifold with boundary cannot have a metric of positive $m$-intermediate…

In this paper, we establish a Liouville type rigidity result for a class of asymptotically hyperbolic non-compact Einstein metrics defined on manifolds of dimension $d\ge 5$ extending the earlier result in dimension $d=4$.

Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study the $(m,\rho)$-quasi-Einstein structure on a contact metric manifold. First, we prove that if…

In this paper, we extend Su-Zhang's Cheeger-Mueller type theorem for symmetric bilinear torsions to manifolds with boundary in the case that the Riemannian metric and the non-degenerate symmetric bilinear form are of product structure near…

We investigate the finiteness structure of a complete non-compact $n$-dimensional Riemannian manifold $M$ whose radial curvature at a base point of $M$ is bounded from below by that of a non-compact von Mangoldt surface of revolution with…

In this paper, we first prove a compactness theorem for the space of closed embedded $f$-minimal surfaces of fixed topology in a closed three-manifold with positive Bakry-\'{E}mery Ricci curvature. Then we give a Lichnerowicz type lower…

It is shown that in every dimension n=3j+2, j=1,2,3,..., there exist compact pseudo-Riemannian manifolds with parallel Weyl tensor, which are Ricci-recurrent, but neither conformally flat nor locally symmetric, and represent all indefinite…

We show that if a manifold M admits a contact structure, then so does M\times S^2. Our proof relies on surgery theory, a theorem of Eliashberg on contact surgery and a theorem of Bourgeois showing that if M admits a contact structure then…