arXiv research

New Einstein metrics found from para-Sasaki-like Riemannian manifolds.

Study on Clairaut maps from nearly Kahler to Riemannian manifolds.

This study examines Clairaut slant Riemannian maps from Riemannian to Kähler manifolds.

A Sasaki-like almost contact complex Riemannian manifold is defined as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. Explicit compact and non-compact examples are given. A canonical construction producing a Sasaki-like almost contact complex Riemannian ma…

As a generalization of anti-invariant Riemannian submersions, we introduce anti-invariant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give examples and investigate the geometry of foliations which are arisen from the definition of an anti-Riemannian map. Then we give a decomposition theo…

Definition of $({\cal T}_{a},{\cal T}_{b})$-pseudosymmetric semi-Riemannian manifold is given. $({\cal T}_{a},{\cal T}_{b})$-pseudosy mmetric $(N(k),ξ)$-semi-Riemannian manifolds are classified. Some results for ${\cal T}_{a}$-pseudosymmetric $(N(k),ξ)$-semi-Riemannian manifolds are obtained. $({\cal T}_{a},{\cal T}_{b…

New examples of hyperbolic Riemannian manifolds proven.

$(N(k),ξ)$-semi-Riemannian manifolds are defined. Examples and properties of $(N(k),ξ)$-semi-Riemannian manifolds are given. Some relations involving ${\cal T}_{a}$-curvature tensor in $(N(k),ξ)$-semi-Riemannian manifolds are proved. $ξ$-${\cal T}_{a}$-flat $(N(k),ξ)$-semi-Riemannian manifolds are defined. It is proved…

Study on Riemannian submersions from nearly Kaehler manifolds.

Study on CR-lightlike submanifolds in golden semi-Riemannian manifolds.

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold $(M,g)$ is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of $(M,g)$. We characterize the following simply connected pseudo-Riemannian manifolds admitting such subbundles in terms of their…

The paper characterizes metallic pseudo-Riemannian manifolds using conjugate connections and tensor structures.

There are many equivalent definitions of Riemannian geodesics. They are naturally generalised to sub-Riemannian manifold, but become non-equivalent. We give a review of different definitions of geodesics of a sub-Riemannian manifold and interrelation between them. We recall three variational definitions of geodesics as…

We study a new class of rank two sub-Riemannian manifolds encompassing Riemannian manifolds, CR manifolds with vanishing Webster-Tanaka torsion, orthonormal bundles over Riemannian manifolds, and graded nilpotent Lie groups of step two. These manifolds admit a canonical horizontal connection and a canonical sub-Laplaci…

Holonomy groups of K-contact sub-Riemannian manifolds are studied.

In this paper, we study slant submanifolds of Riemannian manifolds with Golden structure. A Riemannian manifold $(\tilde{M},\tilde{g},{\varphi})$ is called a Golden Riemannian manifold if the $(1,1)$ tensor field ${\varphi}$ on $\tilde{M}$ is a golden structure, that is ${\varphi}^{2}={\varphi}+I$ and the metric $\tild…

Method approximates Riemannian barycenter on manifolds.

We prove conformal versions of the local decomposition theorems of de Rham and Hiepko of a Riemannian manifold as a Riemannian or a warped product of Riemannian manifolds. Namely, we give necessary and sufficient conditions for a Riemannian manifold to be locally conformal to either a Riemannian or a warped product. We…

We introduce slant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We survey main results of slant Riemannian submersions defined on Sasakian manifolds. We also give an example of such slant submersions.

Two-root Riemannian manifolds have no odd-dimensional examples.

The purpose of this paper is to study anti-invariant Riemannian submersions from Kenmotsu manifolds onto Riemannian manifolds. Several fundamental results in this respect are proved. The integrability of the distributions and the geometry of foliations are investigated. We proved that there do not exist (anti-invariant…

In this paper, we consider critical maps of a horizontal energy functional for maps from a sub-Riemannian manifold to a Riemannian manifold. These critical maps are referred to as subelliptic harmonic maps. In terms of the subelliptic harmonic map heat flow, we investigate the existence problem for subelliptic harmonic…

A {\em 2-Riemannian manifold} is a differentiable manifold exhibiting a 2-inner product on each tangent space. We first study lower dimensional 2-Riemannian manifolds by giving necessary and sufficient conditions for flatness. Afterward we associate to each 2-Riemannian manifold a unique torsion free compatible pseudoc…

We prove that the L^2 Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold induces a metric space structure. As the L^2 metric is a weak Riemannian metric, this fact does not follow from general results. In addition, we prove several results on the exponentia…

Rigidity of Wasserstein spaces over Riemannian manifolds

The authors first in this paper define a semi-symmetric metric non-holonomic connection (called in briefly a semi-sub-Riemannian connection) on sub-Riemannian manifolds, and study the relations between sub-Riemannian connections and semi-sub-Riemannian connections. An invariant under a connection transformation $\nabla…

Study geodesic complexity in homogeneous Riemannian manifolds.

The paper studies Riemannian maps with Ricci soliton base manifolds.

The paper studies bi-slant Riemannian maps to Kenmotsu manifolds and derives inequalities.

Study on pseudo-Riemannian Bertrand manifolds finds no closed movement systems.

Optimizes shapes on non-standard manifolds.

In the present paper we prove Liouville-type theorems: non-existence theorems for some complete Riemannian almost product manifolds and special mappings of complete Riemannian manifolds which generalize similar results for compact manifolds.

We extend Gaussian Differential Privacy to curved Riemannian manifolds.

Smooth manifolds from locally homogeneous spaces.

In this paper, we derived biharmonic equations for pseudo-Riemannian submanifolds of pseudo-Riemannian manifolds which includes the biharmonic equations for submanifolds of Riemannian manifolds as a special case. As applications, we proved that a pseudo-umbilical biharmonic pseudo-Riemannian submanifold of a pseudo-Rie…

The aim of our paper is to focus on some properties of slant and semi-slant submanifolds of metallic Riemannian manifolds. We give some characterizations for submanifolds to be slant or semi-slant submanifolds in metallic or Golden Riemannian manifolds and we obtain integrability conditions for the distributions involv…

There is a well developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian manifolds, but some require additional hypotheses. The topics discussed are homogeneity, geodesic completeness, the geodesic orbit…

RIG extends IG to Riemannian manifolds for explainable AI.

The authors define a SNS (semi-nearly-sub)-Riemannian connection on nearly sub-Riemannian manifolds and study the geometric properties of such a connection, and obtain the natures of horizontal curvature tensors between horizontal sub-Riemannian connection and SNS-Riemannian connection. The authors further investigate …

A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.

Study approximates Riemannian manifolds using polyhedra.

B. Sahin [9] introduced the notion of anti-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. In the present paper we extend the notion of anti-invariant and Lagrangian Riemannian submersions (a special anti-invariant Riemannian submersion) to the case of locally conformal Kaehl…

Survey on gluing constructions under lower curvature bounds.

This paper generalizes biharmonic Riemannian submersions to higher dimensions.

Study finds bounds for fundamental tone on special Riemannian manifolds.

In spin geometry, traceless cyclic homogeneous Riemannian manifolds equipped with a homogeneous spin structure can be viewed as the simplest manifolds after Riemannian symmetric spin spaces. In this paper, we give some characterizations and properties of cyclic and traceless cyclic homogeneous Riemannian manifolds and …

We introduce anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We survey main results of anti-invariant Riemannian submersions defined on Sasakian manifolds. We investigate necessary and sufficient condition for an anti-invariant Riemannian submersion to be totally geodesic and ha…

The paper explores F-manifolds and metrics, constructing canonical structures.