Results 1  10
of
596
Bachflat gradient steady Ricci solitons
 Calc. Var. Partial Differential Equations
, 2014
"... Abstract. In this paper we prove that any ndimensional (n ≥ 4) complete Bachflat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a threedimensional gradient steady Ricci soliton with divergencefree Bach tensor is either flat or is ..."
Abstract

Cited by 16 (8 self)
 Add to MetaCart
if there exists a smooth function f on Mn such that the Ricci tensor Rij of the metric gij satisfies the equation Rij +∇i∇jf = ρ gij for some constant ρ. For ρ = 0 the Ricci soliton is steady, for ρ> 0 it is shrinking and for ρ < 0 expanding. The function f is called a potential function of the gradient
Curvature tensor under the Ricci flow
"... Abstract. Consider the unnormalized Ricci flow (gij)t = −2Rij for t ∈ [0, T), where T < ∞. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times t ∈ [0, T), then the solution can be extended beyond T. We prove that if the Ricci curvature is unifo ..."
Abstract

Cited by 34 (2 self)
 Add to MetaCart
Abstract. Consider the unnormalized Ricci flow (gij)t = −2Rij for t ∈ [0, T), where T < ∞. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times t ∈ [0, T), then the solution can be extended beyond T. We prove that if the Ricci curvature
Curvature tensor under the Ricci flow
, 2008
"... Consider the unnormalized Ricci flow (gij)t = −2Rij for t ∈ [0, T), where T < ∞. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times t ∈ [0, T) then the solution can be extended beyond T. We prove that if the Ricci curvature is uniformly bounde ..."
Abstract
 Add to MetaCart
Consider the unnormalized Ricci flow (gij)t = −2Rij for t ∈ [0, T), where T < ∞. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times t ∈ [0, T) then the solution can be extended beyond T. We prove that if the Ricci curvature is uniformly
Curvature tensor under the Ricci flow
, 2004
"... Consider the unnormalized Ricci flow (gij)t = −2Rij for t ∈ [0, T), where T < ∞. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times t ∈ [0, T) then the solution can be extended beyond T. We prove that if the Ricci curvature is uniformly bounde ..."
Abstract
 Add to MetaCart
Consider the unnormalized Ricci flow (gij)t = −2Rij for t ∈ [0, T), where T < ∞. Richard Hamilton showed that if the curvature operator is uniformly bounded under the flow for all times t ∈ [0, T) then the solution can be extended beyond T. We prove that if the Ricci curvature is uniformly
Deforming metrics in the direction of their Ricci tensors
 SERIES IN GEOMETRY AND TOPOLOGY’ 37
, 2003
"... In [4], R. Hamilton has proved that if a compact manifold M of dimension three admits a C ∞ Riemannian metric g0 with positive Ricci curvature, then it also admits a metric g with constant positive sectional curvature, and is thus a quotient of the sphere S³. In fact, he shows that the original metr ..."
Abstract

Cited by 137 (0 self)
 Add to MetaCart
In [4], R. Hamilton has proved that if a compact manifold M of dimension three admits a C ∞ Riemannian metric g0 with positive Ricci curvature, then it also admits a metric g with constant positive sectional curvature, and is thus a quotient of the sphere S³. In fact, he shows that the original
On the conditions to extend Ricci flow
 Dan Knopf) University of Texas
"... Consider {(M n, g(t)), 0 ≤ t < T < ∞} as an unnormalized Ricci flow solution: dgij = −2Rij for t ∈ [0, T). Richard Hamilton shows that if the dt curvature operator is uniformly bounded under the flow for all t ∈ [0, T) then the solution can be extended over T. Natasa Sesum proves that a unifor ..."
Abstract

Cited by 19 (5 self)
 Add to MetaCart
Consider {(M n, g(t)), 0 ≤ t < T < ∞} as an unnormalized Ricci flow solution: dgij = −2Rij for t ∈ [0, T). Richard Hamilton shows that if the dt curvature operator is uniformly bounded under the flow for all t ∈ [0, T) then the solution can be extended over T. Natasa Sesum proves that a
Comparison Geometry for the BakryEmery Ricci tensor
"... For Riemannian manifolds with a measure (M, g, e −f dvolg) we prove mean curvature and volume comparison results when the ∞BakryEmery Ricci tensor is bounded from below and f is bounded or ∂rf is bounded from below, generalizing the classical ones (i.e. when f is constant). This leads to extension ..."
Abstract

Cited by 77 (7 self)
 Add to MetaCart
For Riemannian manifolds with a measure (M, g, e −f dvolg) we prove mean curvature and volume comparison results when the ∞BakryEmery Ricci tensor is bounded from below and f is bounded or ∂rf is bounded from below, generalizing the classical ones (i.e. when f is constant). This leads
Some geometric properties of the BakryÉmeryRicci tensor
 Comment. Math. Helv
"... Abstract. The BakryÉmery tensor gives an analog of the Ricci tensor for a Riemannian manifold with a smooth measure. We show that some of the topological consequences of having a positive or nonnegative Ricci tensor are also valid for the BakryÉmery tensor. We show that the BakryÉmery tensor is n ..."
Abstract

Cited by 52 (2 self)
 Add to MetaCart
Abstract. The BakryÉmery tensor gives an analog of the Ricci tensor for a Riemannian manifold with a smooth measure. We show that some of the topological consequences of having a positive or nonnegative Ricci tensor are also valid for the BakryÉmery tensor. We show that the BakryÉmery tensor
The Ricci tensor of SU(3)manifolds
 J. Geom. Phys
"... Abstract. Following the approach of Bryant [9] we study the intrinsic torsion of a SU(3)manifold deriving a number of formulae for the Ricci and the scalar curvature in terms of torsion forms. As a consequence we prove that in some special cases the Einstein condition forces the vanishing of the in ..."
Abstract

Cited by 22 (1 self)
 Add to MetaCart
Abstract. Following the approach of Bryant [9] we study the intrinsic torsion of a SU(3)manifold deriving a number of formulae for the Ricci and the scalar curvature in terms of torsion forms. As a consequence we prove that in some special cases the Einstein condition forces the vanishing
Results 1  10
of
596