Remarks on scalar curvature of gradient Yamabe solitons with non-positive Ricci curvature

2022 ◽  
Vol 80 ◽  
pp. 101843
Author(s):  
Antonio W. Cunha
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Positive Ricci Curvature ◽  
Yamabe Solitons

scholarly journals Estimates on the non-compact expanding gradient Ricci solitons

2013 ◽  
Vol 21 (3) ◽  
pp. 95-102
Author(s):  
Xiang Gao ◽  
Qiaofang Xing ◽  
Rongrong Cao
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Linear Growth ◽  
Ricci Soliton ◽  
Potential Functions ◽  
Ricci Solitons ◽  
Positive Ricci Curvature ◽  
Gradient Ricci Soliton ◽  
Gradient Ricci Solitons ◽  
Normal Geodesic

Abstract In this paper, we deal with the complete non-compact expanding gradient Ricci soliton (Mn,g) with positive Ricci curvature. On the condition that the Ricci curvature is positive and the scalar curvature approaches 0 towards infinity, we derive a useful estimate on the growth of potential functions. Based on this and under the same assumptions, we prove that ∫t0 Rc (γ'(s) , γ' (s))ds and ∫t0 Rc (γ' (,s). v)ds at least have linear growth, where 7(5) is a minimal normal geodesic emanating from the point where R obtains its maximum. Furthermore, some other results on the Ricci curvature are also obtained.

Chen inequalities on lightlike hypersurfaces of a GRW spacetime

2021 ◽  
Author(s):  
Nergi̇z (Önen) Poyraz
Keyword(s):  
Scalar Curvature ◽  
Ricci Curvature ◽  
Lightlike Hypersurfaces ◽  
Chen Inequality

In this paper, we introduce [Formula: see text]-Ricci curvature and [Formula: see text]-scalar curvature on lightlike hypersurfaces of a GRW spacetime. Using these curvatures, we establish some inequalities for lightlike hypersurfaces of a GRW spacetime. Using these inequalities, we obtain some characterizations on lightlike hypersurfaces. We also get Chen–Ricci inequality and Chen inequality on a screen homothetic lightlike hypersurfaces of a GRW spacetime.

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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