Considering the scale dependent effective spacetimes implied by functional renormalization group in d-dimensional Quantum Einstein Gravity, we discuss representation of entire evolution histories means a single, (d + 1)-dimensional manifold furnished with fixed (pseudo-) Riemannian structure. This "scale-space-time" carries natural foliation whose leaves are ordinary seen at given resolution. W...

The purpose of this article is to explain how pseudo-holomorphic curves in a symplectic 4-manifold can be constructed from solutions to the Seiberg-Witten equations. As such, the main theorem proved here (Theorem 1.3) is an existence theorem for pseudo-holomorphic curves. This article thus provides a proof of roughly half of the main theorem in the announcement [T1]. That theorem, Theorem 4.1, ...

A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point of the manifold is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for manifolds of nonnegative scalar curvature and for some other classes of manifolds, but is not true in general: there exists a family of homog...

In this paper we introduce notion of Ricci solitons in -para Kenmotsu manifold with semi -symmetric metric connection. We have found the relations between curvature tensor, tensors and scalar semi-symmetic connection.We proved that 3-dimensional connection is an -Einstein soliton defined on named expanding steady respect to value constant.It Conharmonically flat semi-symmetric manifold.

Abstract. The present paper discusses the question of formulating and solving minimal-distance problems over the group-manifold of real symplectic matrices. In order to tackle the related optimization problem, the real symplectic group is regarded as a pseudo-Riemannian manifold and a metric is chosen that affords the computation of geodesic arcs in closed forms. Then, the considered minimal-di...

Let X be a compact Kähler manifold and let L be a pseudoeffective line bundle on X with singular metric φ. We first define a notion of numerical dimension of the pseudo-effective pair (L,φ) and then discuss the properties of it. We prove also a very general KawamataViehweg-Nadel type vanishing theorem on an arbitrary compact Kähler manifold.

In this article, the aim is to introduce a para-Sasakian manifold with a canonical paracontact connection. It is shown that φ−conharmonically flat , φ−W2 flat and φ−pseudo projectively flat para-Sasakian manifolds with respect to canonical paracontact connection are all η−Einstein manifolds. Also, we prove that quasi-pseudo projectively flat para-Sasakian manifolds are of constant scalar curvat...

We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyperpseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with constant scalar and ⋆-scalar curvature.

In this article we show that every smooth closed oriented fourmanifold admits a decomposition into two submanifolds along common boundary. Each of these submanifolds is a complex manifold with pseudo-convex boundary. This imply, in particular, that every smooth closed simply-connected four-manifold is a Stein domain in the the complement of a certain contractible 2-complex.

We give an elementary proof of the fact that any 4-dimensional para-Hermitian manifold admits a unique para-Kähler–Weyl structure. We then use analytic continuation to pass from the para-complex to the complex setting and thereby show that any 4-dimensional pseudo-Hermitian manifold also admits a unique Kähler–Weyl structure.