Results 91 to 100 of about 427,064 (305)
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
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
Quantitative Biology, Volume 13, Issue 3, September 2025.Abstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Peng Zhang +3 more
wiley +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
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
On the isoperimetric Riemannian Penrose inequality
Communications on Pure and Applied Mathematics, Volume 78, Issue 5, Page 1042-1085, May 2025.Abstract We prove that the Riemannian Penrose inequality holds for asymptotically flat 3‐manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the ADM$\operatorname{ADM}$ mass being a well‐defined geometric invariant.
Luca Benatti +2 more
wiley +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