Ricci almost solitons with associated projective vector field

A Ricci almost soliton whose associated vector field is projective is shown to have vanishing Cotton tensor, divergence-free Bach tensor and Ricci tensor as conformal Killing. For the compact case, a sharp inequality is obtained in terms of scalar curvature.We show that every complete gradient Ricci soliton is isometric to the Riemannian product of a Euclidean space and an Einstein space. A complete K-contact Ricci almost soliton whose associated vector field is projective is compact Einstein and Sasakian.

GENUS MINIMAL k-NOIDS AND SADDLE TOWERS IN

For each $k\geq 3$ , we construct a $1$ -parameter family of complete properly Alexandrov-embedded minimal surfaces in the Riemannian product space $\mathbb {H}^2\times \mathbb {R}$ with genus $1$ and k embedded ends asymptotic to vertical planes. We also obtain complete minimal surfaces with genus $1$ and $2k$ ends in the quotient of $\mathbb {H}^2\times \mathbb {R}$ by an arbitrary vertical translation. They all have dihedral symmetry with respect to k vertical planes, as well as finite total curvature $-4k\pi $ . Finally, we provide examples of complete properly Alexandrov-embedded minimal surfaces with finite total curvature with genus $1$ in quotients of $\mathbb {H}^2\times \mathbb {R}$ by the action of a hyperbolic or parabolic translation.

The k-almost Yamabe solitons and almost coKähler manifolds

In this paper, we study almost coKähler manifolds admitting [Formula: see text]-almost Yamabe solitons [Formula: see text]. First, we obtain a classification of almost coKähler [Formula: see text]-manifolds admitting nontrivial closed [Formula: see text]-almost Yamabe solitons. Next, we consider an almost [Formula: see text]-coKähler manifold admitting a nontrivial [Formula: see text]-almost Yamabe soliton and prove that it is locally the Riemannian product of an almost Kähler manifold with the real line if the potential vector field [Formula: see text] is collinear with the Reeb vector field. For the potential vector field [Formula: see text] being orthogonal to the Reeb vector field, we also obtain two results.

Warped product bi-slant submanifolds of kenmotsu manifold

In this paper, we obtain several fundamental results of bi-slant submanifolds in a Kenmotsu manifold. Next, we give an example of such submanifolds. Later, we obtain some results of proper bi-slant submanifolds of a Kenmotsu manifold. Here, we show every warped product bi-slant submanifold of a Kenmotsu manifold to be a Riemannian product under some certain conditions.

Study on Twisted Product Almost Gradient Yamabe Solitons

In this paper, we first study gradient Yamabe solitons on the twisted product spaces. Then, we classify and characterize the warped product and twisted product spaces with almost gradient Yamabe solitons. We also study the construction of almost gradient Yamabe solitons in the Riemannian product spaces.

Skew Killing spinors in four dimensions

This paper is devoted to the classification of 4-dimensional Riemannian spin manifolds carrying skew Killing spinors. A skew Killing spinor $$\psi $$ ψ is a spinor that satisfies the equation $$\nabla _X\psi =AX\cdot \psi $$ ∇ X ψ = A X · ψ with a skew-symmetric endomorphism A. We consider the degenerate case, where the rank of A is at most two everywhere and the non-degenerate case, where the rank of A is four everywhere. We prove that in the degenerate case the manifold is locally isometric to the Riemannian product $${\mathbb {R}}\times N$$ R × N with N having a skew Killing spinor and we explain under which conditions on the spinor the special case of a local isometry to $${\mathbb {S}}^2\times {\mathbb {R}}^2$$ S 2 × R 2 occurs. In the non-degenerate case, the existence of skew Killing spinors is related to doubly warped products whose defining data we will describe.

Ricci recurrent almost Kenmotsu 3-manifolds

In this paper, we obtain that a Ricci recurrent 3-dimensional almost Kenmotsu manifold with constant scalar curvature satisfying ??h = 0,h ? 0, is locally isometric to the Riemannian product H2(-4)xR.

Almost quasi-Yamabe solitons on almost cosymplectic manifolds

In this paper, we study almost cosymplectic manifolds admitting almost quasi-Yamabe solitons [Formula: see text]. First, we prove that an almost cosymplectic [Formula: see text]-manifold is locally isomorphic to a Lie group if [Formula: see text] is a nontrivial closed quasi-Yamabe soliton. Next, we consider an almost [Formula: see text]-cosymplectic manifold admitting a nontrivial almost quasi-Yamabe soliton and prove that it is locally the Riemannian product of an almost Kähler manifold with the real line if the potential vector field [Formula: see text] is collinear with the Reeb vector filed. For the potential vector field [Formula: see text] being orthogonal to the Reeb vector filed, we also obtain two results. Finally, for a closed almost quasi-Yamabe soliton on compact [Formula: see text]-cosymplectic manifolds, we prove that it is trivial if [Formula: see text] is nonnegative, where [Formula: see text] is the scalar curvature.