Randers manifolds of positive constant curvature.
Rank and -nullity of contact manifolds.
Real and complex transversely symplectic Anosov flows of dimension five
Nous présentons plusieurs résultats de rigidité concernant les flots d’Anosov admettant transversalement des structures symplectiques réelles ou complexes de dimension .
Real hypersurfaces of indefinite Kähler manifolds.
Reflections with respect to submanifolds in contact geometry
We study to what extent some structure-preserving properties of the geodesic reflection with respect to a submanifold of an almost contact manifold influence the geometry of the submanifold and of the ambient space.
Regularity Theorems in Riemannian Geometry. II. Harmonic Curvature and the Weyl Tensor.
Relative K-stability of extremal metrics
We show that if a polarised manifold admits an extremal metric then it is K-polystable relative to a maximal torus of automorphisms.
Remarks on the Existence Problem of Positive Kähler-Einstein Metrics.
Ricci and scalar curvatures of submanifolds of a conformal Sasakian space form
We introduce a conformal Sasakian manifold and we find the inequality involving Ricci curvature and the squared mean curvature for semi-invariant, almost semi-invariant, -slant, invariant and anti-invariant submanifolds tangent to the Reeb vector field and the equality cases are also discussed. Also the inequality involving scalar curvature and the squared mean curvature of some submanifolds of a conformal Sasakian space form are obtained.
Ricci curvature of submanifolds in Kenmotsu space forms.
Ricci-flat left-invariant Lorentzian metrics on 2-step nilpotent Lie groups
The purpose of this paper is to investigate Ricci-flatness of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups. We first show that if is a Ricci-flat left-invariant Lorentzian metric on a 2-step nilpotent Lie group , then the restriction of to the center of the Lie algebra of is degenerate. We then characterize the 2-step nilpotent Lie groups which can be endowed with a Ricci-flat left-invariant Lorentzian metric, and we deduce from this that a Heisenberg Lie group can be...
Riemannian convexity in programming. II.
Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions
We consider an almost Kenmotsu manifold with the characteristic vector field ξ belonging to the (k,μ)’-nullity distribution and h’ ≠ 0 and we prove that is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, provided that is ξ-Riemannian-semisymmetric. Moreover, if is a ξ-Riemannian-semisymmetric almost Kenmotsu manifold such that ξ belongs to the (k,μ)-nullity distribution, we prove that is...
Riesz means on Lie groups and riemannian manifolds of nonnegative curvature
Rigidity of Einstein manifolds and generalized quasi-Einstein manifolds
We discuss the rigidity of Einstein manifolds and generalized quasi-Einstein manifolds. We improve a pinching condition used in a theorem on the rigidity of compact Einstein manifolds. Under an additional condition, we confirm a conjecture on the rigidity of compact Einstein manifolds. In addition, we prove that every closed generalized quasi-Einstein manifold is an Einstein manifold provided μ = -1/(n-2), λ ≤ 0 and β ≤ 0.
Rigidity of noncompact manifolds with cyclic parallel Ricci curvature
We prove that if M is a complete noncompact Riemannian manifold whose Ricci tensor is cyclic parallel and whose scalar curvature is nonpositive, then M is Einstein, provided the Sobolev constant is positive and an integral inequality is satisfied.