scholarly journals A Note on Lower Bounds Estimates for the Neumann Eigenvalues of Manifolds with Positive Ricci Curvature

2011 ◽  
Vol 37 (1) ◽  
pp. 91-101 ◽  
Author(s):  
Fabrice Baudoin ◽  
Alice Vatamanelu
Keyword(s):  
Ricci Curvature ◽  
Lower Bounds ◽  
Positive Ricci Curvature ◽  
Neumann Eigenvalues

scholarly journals Spaces of positive intermediate curvature metrics

2021 ◽  
Author(s):  
Georg Frenck ◽  
Jan-Bernhard Kordaß
Keyword(s):  
Ricci Curvature ◽  
Lower Bounds ◽  
Riemannian Metrics ◽  
High Dimensional ◽  
Homotopy Groups ◽  
Positive Ricci Curvature ◽  
Spaces Of Metrics

AbstractIn this paper we study spaces of Riemannian metrics with lower bounds on intermediate curvatures. We show that the spaces of metrics of positive p-curvature and k-positive Ricci curvature on a given high-dimensional $$\mathrm {Spin}$$ Spin -manifold have many non-trivial homotopy groups provided that the manifold admits such a metric.

scholarly journals Greatest lower bounds on Ricci curvature of homogeneous toric bundles

2017 ◽  
Vol 28 (04) ◽  
pp. 1750024 ◽  
Author(s):  
Yi Yao
Keyword(s):  
Ricci Curvature ◽  
Lower Bounds ◽  
Line Bundles

We derive a formula of the greatest lower bounds on Ricci curvature of Fano homogeneous toric bundles. A criteria for the ampleness of line bundles over general homogeneous toric bundles is also obtained.

scholarly journals Lower bounds on Ricci flow invariant curvatures and geometric applications

2015 ◽  
Vol 2015 (703) ◽  
Author(s):  
Thomas Richard
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Lower Bounds ◽  
Ricci Flow ◽  
Nonnegative Curvature ◽  
Curvature Operator ◽  
Nonnegative Ricci Curvature ◽  
Invariant Cones

AbstractWe consider Ricci flow invariant cones 𝒞 in the space of curvature operators lying between the cones “nonnegative Ricci curvature” and “nonnegative curvature operator”. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to the Ricci flow has its curvature operator which satisfies

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