Related papers: Product of Almost-Hermitian Manfolds

We study two natural problems concerning the scalar and the Ricci curvatures of the Bismut connection. Firstly, we study an analog of the Yamabe problem for Hermitian manifolds related to the Bismut scalar curvature, proving that, fixed a…

In this paper, we generalize the results in [Y. Wang: Affine connections on singular warped products. Int. J. Geom. Methods Mod. Phys. 18(5), 2150076, (2021).] to singular multiply warped products and singular twisted products. We study…

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…

The main purpose of the present work is to investigate statistical manifolds endowed with almost product structures. We prove that the statistical structure of a para-K\"{a}hler-like statistical manifold of constant curvature in the…

We describe a method of defining a Hermitian metric on Kobayashi hyperbolic manifolds. The metric is distance decreasing under holomorphic mappings, up to a multiplicative constant. This method is distinct from the classical construction of…

In this work, almost product and almost golden structures are studied. Conditions for those structures being Integrable and parallel are investigated. Also harmonicity of a map between almost pruduct or almost golden manifolds with pure or…

In this paper, we will give a horizontal gradient estimate of positive solutions of $\Delta_b u = - \lambda u$ on complete noncompact pseudo-Hermitian manifolds. As a consequence, we recapture the Liouville theorem of positive…

The decomposability of a Cartesian product of two nondecomposable manifolds into products of lower dimensional manifolds is studied. For 3-manifolds we obtain an analog of a result due to Borsuk for surfaces, and in higher dimensions we…

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…

Almost para-Hermitian manifold it is manifold equipped with almost para-complex structure and compatible pseudo-metric of neutral signature. It is considered a class of immersions of almost para-Hermitian manifolds into almost…

We introduce partial secondary invariants associated to complete Riemannian metrics which have uniformly positive scalar curvature outside a prescribed subset on a spin manifold. These can be used to distinguish such Riemannian metrics up…

Almost contact complex Riemannian manifolds, known also as almost contact B-metric manifolds, are in principle equipped with a pair of mutually associated pseudo-Riemannian metrics. Each of these metrics is specialized here as a Yamabe…

The notion of relativistic observer is confronted with Naveira's classification of (pseudo-)Riemannian almost-product structures on space-time manifolds. Some physical properties and their geometrical counterparts are shortly discussed.

We discover a "no semistability at infinity" phenomenon for complete Calabi-Yau metrics asymptotic to cones, by eliminating the possible appearance of an intermediate K-semistable cone in the 2-step degeneration theory developed by…

This note is concerned in so called harmonic complex structures introduced by the author previously. I will recall some previous results and emphasize the motivation: Provide an attempt to a fundamental problem in geometry--determining the…

The spaces of Riemannian metrics on a closed manifold $M$ are studied. On the space ${\mathcal M}$ of all Riemannian metrics on $M$ the various weak Riemannian structures are defined and the corresponding connections are studied. The space…

Recently Y{\"u}ksel et. al. \cite{SY} shows that there doesn't exist any proper semi-slant warped product submanifolds in a Lorentzian paracosymplectic manifold. In the present article, we first define and give preparatory lemmas for a new…

We study one class of linear sigma models and their T-dualized theories for noncompact Calabi-Yau manifolds. In the low energy limit, we find that this system has various massless effective theories with orbifolding symmetries. This…

We discuss the extent to which numerical techniques for computing approximations to Ricci-flat metrics can be used to investigate hierarchies of curvature scales on Calabi-Yau manifolds. Control of such hierarchies is integral to the…

We introduce asymptotic-M\"obius (AM) maps, a large-scale analogue of quasi-M\"obius maps tailored to geometric group theory. AM-maps capture coarse cross-ratio behavior for configurations of points that lie far apart, providing a notion of…