相关论文: Local properties of almost-Riemannian structures i…

It is well known that one can parameterize 2-D Riemannian structures by conformal transformations and diffeomorphisms of fiducial constant curvature geometries; and that this construction has a natural setting in general relativity theory…

Let $(M,g)$ be an n-dimensional Riemannian manifold and $T^{*}M$ be its cotangent bundle equipped with a Riemannian metric of Cheeger Gromoll type which rescale the horizontal part by a nonzero differentiable function. The main purpose of…

The generalized partially linear models on Riemannian manifolds are introduced. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for response variables…

In this paper we study invariant almost Hermitian geometry on generalized flag manifolds. We will focus on providing examples of K\"ahler like scalar curvature metric, that is, almost Hermitian structures $(g,J)$ satisfying $s=2s_{\rm C}$,…

A 4-dimensional Riemannian manifold equipped with a circulant structure, which is an isometry with respect to the metric and its fourth power is the identity, is considered. The almost product manifold associated with the considered…

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,…

We introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations which are arisen from the definition of a Riemannian submersion and find…

This article is the introductory part of authors PhD thesis. The article presents a new coordinate invariant definition of quasiregular and quasiconformal mappings on Riemannian manifolds that generalizes the definition of quasiregular…

We study curvature properties of four-dimensional almost Hermitian manifolds with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. We give local structure theorems for such Kaehler manifolds, and find out several…

We consider a unit normal vector field of (local) hyperfoliation on a given Riemannian manifold as a submanifold in the unit tangent bundle with Sasaki metric. We give an explicit expression of the second fundamental form for this…

Let $(M,I)$ be an almost complex 6-manifold. The obstruction to integrability of almost complex structure (so-called Nijenhuis tensor) maps a 3-dimensional bundle to a 3-dimensional one. We say that Nijenhuis tensor is non-degenerate if it…

We review the construction of almost contact metric (three-) structures, abbreviated ACM(3)S, on manifolds with a $G_2$ structure. These are of interest for certain supersymmetric configurations in string and M-theory. We compute the…

We establish a uniformization result for metric surfaces - metric spaces that are topological surfaces with locally finite Hausdorff 2-measure. Using the geometric definition of quasiconformality, we show that a metric surface that can be…

This text is an introductory review of the basic concepts of the theory of semi-Riemannian geometry on real finite-dimensional manifolds without boundary.

We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic…

In the present paper we deal with (local) infinitesimal isometries of special sub-Riemannian manifolds (a contact and oriented sub-Riemannian manifold is called special if the Reeb vector field is an isometry). The objective of the paper is…

The twistor space \Z of an oriented Riemannian 4-manifold M admits a natural 1-parameter family of Riemannian metrics h_t compatible with the almost complex structures J_1 and J_2 introduced, respectively, by Atiyah, Hitchin and Singer, and…

In this paper we study a Riemanian metric on the tangent bundle $T(M)$ of a Riemannian manifold $M$ which generalizes Sasaki metric and Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers…

For k at least 2, we exhibit complete k-curvature homogeneous neutral signature pseudo-Riemannian manifolds which are not locally affine homogeneous (and hence not locally homogeneous). The curvature tensor of these manifolds is modeled on…

A natural metric on the space of all almost hermitian structures on a given manifold is investigated.