Related papers: Hermitian Manifolds with Flat Associated Connectio…

We show that locally conformally flat quasi-Einstein manifolds are globally conformally equivalent to a space form or locally isometric to a $pp$-wave or a warped product.

We prove several K\"ahlerness criteria for compact Hermitian surfaces under semi-definiteness assumptions on natural Ricci curvatures of the Strominger-Bismut connection. The key tools for proving these results are explicit identities…

The Schur's theorem of antiholomorphic type is proved for arbitrary almost Hermitian manifolds, namely: If a connected almost Hermitian manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional…

This is the first of two companion papers in which a thorough study of the normal form and the first integrability conditions arising from {\em bi-conformal vector fields} is presented. These new symmetry transformations were introduced in…

Let $\pi : \mathcal X \to S$ be a local universal family of compact Ricci-flat K\"ahler manifolds over a smooth base $S$. The complexified K\"ahler cones of each fiber of the family form a holomorphic fiber bundle $\mathcal K \to S$. We…

We study conformal product structures on compact reducible Riemannian manifolds, and show that under a suitable technical assumption, the underlying Riemannian mani\-folds are either conformally flat, or triple products, \emph{i.e.} locally…

The curvature tensor of a symplectic connection, as well as its covariant derivatives, satisfy certain identities that hold on any manifold of dimension less than or equal to a fixed n. In this paper, we prove certain results regarding…

We investigate the local geometry of a pair of independent contact structures on 3-manifolds under maps that independently preserve each contact structure. We discover that such maps are homotheties on the contact 1-forms and we discover…

In this paper we study sectional curvature of invariant hyper-Hermitian metrics on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. We give the Levi-Civita connections and explicit formulas for…

We study Hermitian metrics with a Gauduchon connection being "K\"ahler-like", namely, satisfying the same symmetries for curvature as the Levi-Civita and Chern connections. In particular, we investigate $6$-dimensional solvmanifolds with…

In this paper, we construct metallic K\"ahler and nearly metallic K\"ahler structures on Riemanian manifolds. For such manifolds with these structures, we study curvature properties. Also we describe linear connections on the manifold,…

This paper presents two results in the realm of conformal Kaehler submanifolds. These are conformal immersions of Kaehler manifolds into the standard flat Euclidean space. The proofs are obtained by making a rather strong use of several…

An identity of conformal-projective curvature tensor of a statistical manifold is studied in this paper. The relation between the constancy of curvature and conformal-projective flatness of statistical manifolds is also discussed.

A locally metric connection on a smooth manifold $M$ is a torsion-free connection $D$ on $TM$ with compact restricted holonomy group $\mathrm{Hol}_0(D)$. If the holonomy representation of such a connection is irreducible, then $D$ preserves…

A hypercomplex manifold is a manifold equipped with a triple of complex structures satisfying the quaternionic relations. A holomorphic Lagrangian variety on a hypercomplex manifold with trivial canonical bundle is a holomorphic subvariety…

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 {\theta}-holomorphic sectional curvature for a number {\theta} in (0,{\pi}/2) then M is of…

The geometrical description of a Hilbert space asociated with a quantum system considers a Hermitian tensor to describe the scalar inner product of vectors which are now described by vector fields. The real part of this tensor represents a…

A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a…

We study the basic geometric properties of an indefinite locally conformal Kaehler manifold.

We establish that Hitchin's connection exist for any rigid holomorphic family of Kahler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove…