arXiv research

Two families of curvature inhomogeneous manifolds with constant Ricci eigenvalues are constructed.

We prove the linear stability of Schwarzschild-Tangherlini spacetimes and their Anti-de Sitter counterparts under Ricci flow for a special class of perturbations. This is useful in the choice of suitable initial conditions in numerical Ricci-flow-based algorithms for obtaining new solutions to the Einstein equation whe…

The study explores slant submanifolds in Golden Riemannian manifolds.

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…

Study properties of hemi-slant submanifolds in metallic Riemannian manifolds.

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…

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…

The study explores different definitions of geodesics in sub-Riemannian geometry.

Study extends Riemannian submersion concepts to locally conformal Kaehler manifolds.

$(N(k),ξ)$-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…

New examples of hyperbolic Riemannian manifolds proven.

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…

Study compares H-type sub-Riemannian manifolds using uniform metrics.

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

Study on submanifolds in metallic Riemannian manifolds.

The study explores properties of slant and semi-slant submanifolds in metallic Riemannian manifolds.

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.

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…

The paper proves Eells-Sampson type theorems for subelliptic harmonic maps.

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

Study metallic Riemannian structures on submanifolds of Riemannian manifolds.

Introduces conformal Riemannian morphisms generalizing various Riemannian concepts.

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.

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…

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 the geometry of transversal lightlike submanifolds in Metallic Semi-Riemannian manifolds.

This paper surveys parallel submanifolds in Riemannian and pseudo-Riemannian manifolds.

Study projective semi-symmetric connections on Riemannian manifolds.

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

We extend Gaussian Differential Privacy to curved Riemannian manifolds.

Optimizes shapes on non-standard manifolds.

Note shows Cheng-Yau estimate for Carnot groups and sub-Riemannian manifolds.

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…

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.

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…