Results 71 to 80 of about 346,734 (227)

Natural Connections on Riemannian Product Manifolds [PDF]

arXiv, 2011
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.
arxiv  

Shortest and Straightest Geodesics in Sub-Riemannian Geometry [PDF]

, 2019
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.
arxiv   +1 more source

Rigidity and Triviality of Gradient r-Almost Newton-Ricci-Yamabe Solitons

Mathematics
In this paper, we develop the concept of gradient r-Almost Newton-Ricci-Yamabe solitons (in brief, gradient r-ANRY solitons) immersed in a Riemannian manifold.
Mohd Danish Siddiqi, Fatemah Mofarreh
doaj   +1 more source

Anti-invariant Riemannian maps from almost Hermitian manifolds [PDF]

arXiv, 2012
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.
arxiv  

The spectral geometry of a Riemannian manifold

, 1975
We adopt the convention of summing over repeated indices except where otherwise indicated. Let (g) denote the inverse of the matrix (g^ ). Let V be a smooth vector bundle over M and let D be a second order differential operator on V.
P. Gilkey
semanticscholar   +1 more source

On the sectional curvature of lightlike submanifolds

Journal of Inequalities and Applications, 2016
The main purpose of this paper is to show how to obtain rigidity theorems with the help of curvature invariants in submanifolds of a semi-Riemannian manifold.
Erol Kılıç, Mehmet Gülbahar
doaj   +1 more source

The left-invariant contact metric structure on the Sol manifold

Учёные записки Казанского университета: Серия Физико-математические науки, 2020
Among the known eight-dimensional Thurston geometries, there is a geometry of the Sol manifold – a Lie group consisting of real special matrices. For a left-invariant Riemannian metric on the Sol manifold, the left shift group is a maximal simple ...
V.I. Pan’zhenskii, A.O. Rastrepina
doaj   +1 more source

On $(N(k),ξ)$-semi-Riemannian manifolds: Semisymmetries [PDF]

arXiv, 2012
$(N(k),\xi)$-semi-Riemannian manifolds are defined. Examples and properties of $(N(k),\xi)$-semi-Riemannian manifolds are given. Some relations involving ${\cal T}_{a}$-curvature tensor in $(N(k),\xi)$-semi-Riemannian manifolds are proved. $\xi $-${\cal T}_{a}$-flat $(N(k),\xi)$-semi-Riemannian manifolds are defined.
arxiv  

On δ-homogeneous Riemannian manifolds [PDF]

Doklady Mathematics, 2007
AbstractWe study in this paper previously defined by V.N. Berestovskii and C.P. Plaut δ-homogeneous spaces in the case of Riemannian manifolds and prove that they constitute a new proper subclass of geodesic orbit (g.o.) spaces with non-negative sectional curvature, which properly includes the class of all normal homogeneous Riemannian spaces.
V. N. Berestovskiĭ, Yu. G. Nikonorov
openaire   +3 more sources

Eells-Sampson type theorems for subelliptic harmonic maps from sub-Riemannian manifolds [PDF]

arXiv, 2019
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 maps.
arxiv