Results 11 to 20 of about 2,699,199 (290)
On the total absolute curvature of manifolds immersed in Riemannian manifold [PDF]
Kodai Mathematical Journal, 1967 Willmore and Saleemi [12] had generalized Chern-Lashof s results by definingthe total curvature of an orientable manifold immersed in a Riemannian manifold,but unfortunately, the results contained mistakes, and hence they are false.The object of this paper is to generalize the Lipschitz-Killing curvature to themanifolds immersed in a complete, simply ...
Bang‐Yen Chen
openalex +6 more sources
A note on curvature of Riemannian manifolds
Journal of Mathematical Analysis and Applications, 2013 Abstract With the aid of the weak maximum principle at infinity we give some sufficient conditions for Riemannian manifolds to be either Einstein or of constant sectional curvature.
P. Mastrolia, D.D. Monticelli, M. Rigoli
openaire +3 more sources
Almost-Riemannian manifolds do not satisfy the curvature-dimension condition [PDF]
Calc Var Partial Differ Equ, 2022 The Lott–Sturm–Villani curvature-dimension condition $$\textsf{CD}(K,N)$$ CD ( K , N ) provides a synthetic notion for a metric measure space to have curvature bounded from below by K and dimension bounded from above by N .
Mattia Magnabosco, T. Rossi
semanticscholar +2 more sources
Prescribing the curvature of Riemannian manifolds with boundary [PDF]
Calculus of Variations and Partial Differential Equations, 2019 Let $M$ be a compact connected surface with boundary. We prove that the signal condition given by the Gauss-Bonnet theorem is necessary and sufficient for a given smooth function $f$ on $\partial M$ (resp. on $M$) to be geodesic curvature of the boundary (resp. the Gauss curvature) of some flat metric on $M$ (resp. metric on $M$ with geodesic boundary).
Tiarlos Cruz, Feliciano Vitorio
openaire +4 more sources
Convergence of riemannian manifolds with integral bounds on curvature. I [PDF]
, 1992 © Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1992, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www. elsevier.com/locate/ansens) implique l’accord avec les conditions générales
Deane Yang
openalex +2 more sources
On curvature tensors of Norden and metallic pseudo-Riemannian manifolds
Complex Manifolds, 2019 We study some properties of curvature tensors of Norden and, more generally, metallic pseudo-Riemannian manifolds. We introduce the notion of J-sectional and J-bisectional curvature of a metallic pseudo-Riemannian manifold (M, J, g) and study their ...
Blaga Adara M., Nannicini Antonella
doaj +2 more sources
Sectional Curvature in Riemannian Manifolds
The Mathematica Journal, 2020 The metric structure on a Riemannian or pseudo-Riemannian manifold is entirely determined by its metric tensor, which has a matrix representation in any given chart.
Francis Owen +2 more
openaire +2 more sources
Manifolds of Riemannian metrics with prescribed scalar curvature [PDF]
, 1974 THEOREM 2. Assume J * V 0 . Writing UtQ=(je a o\0 )U&9 J(\ is the disjoint union of closed submanifolds. REMARK. If d i m M = 2 , e^J=^" 8 , and if d i m M = 3 , the hypothesis that 1F*J£0 can be dropped. The proof of Theorem 1 also allows us to conclude
Arthur E. Fischer, Jerrold E. Marsden
openalex +2 more sources
On the curvatures of Riemannian manifolds [PDF]
Illinois Journal of Mathematics, 1966 J. A. Thorpe
openalex +3 more sources
Complete curvature homogeneous pseudo-Riemannian manifolds [PDF]
Classical and Quantum Gravity, 2004 Update paper to fix misprints in original ...
Peter Gilkey, S Nik evi
openalex +7 more sources