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TOTAL SCALAR CURVATURE AND HARMONIC CURVATURE

Taiwanese Journal of Mathematics, 2014
On a compact n-dimensional manifold, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will be Einstein. This conjecture was proposed in 1984 by Besse, but has yet to be proved.
Gabjin Yun, Jeongwook Chang, Seungsu Hwang   +2 more
exaly   +4 more sources

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On the P-Scalar Curvature

Journal of Geometric Analysis, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Farhan Abedin, Justin Corvino, Corvino Justin   +2 more
exaly   +2 more sources

On symmetric finsler spaces ofHp-scalar curvature and scalar curvature

Periodica Mathematica Hungarica, 1986
A Finsler space \(F_ n\) is said to be of Hp-scalar curvature if \(p\cdot H_{\ell ijr}=k(h_{\ell j} h_{ir}-h_{\ell r} h_{ij})\), where \(H_{\ell ijr}\) is the Berwald h-curvature tensor, p is an operator projecting on the indicatrix, \(h_{ij}\) is the angular metric tensor, and k is the curvature scalar.
Sinha, B. B., Ram, A.
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Prescribing Morse Scalar Curvatures

Milan Journal of Mathematics, 2022
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Prescribed scalar curvature on the $n$ -sphere

Calculus of Variations and Partial Differential Equations, 1996
The authors establish the Morse inequalities for the scalar curvature problem (i.e. The Kazdan-Warner problem) on \(S^3\). This result compliments an earlier existence theorem of \textit{A. Bahri} and \textit{J. M. Coron} [J. Funct. Anal. 95, No. 1, 106-172 (1991; Zbl 0722.53032)].
Schoen, Richard, Zhang, Dong
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S-Curvature, E-Curvature, and Berwald Scalar Curvature of Finsler Spaces

Differential Geometry and its Applications, 2023
This paper deals with the study of \(S\)-curvature, \(E\)-curvature and Berwald scalar curvature for Finsler spaces. More exactly, the author proves that the \(S\)-curvature of a Finsler space vanishes if and only if the \(E\)-curvature vanishes if and only if the Berwald scalar curvature vanishes.
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Gap Extremality for Scalar Curvature

The Journal of Geometric Analysis
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Sun, Yukai, Wang, Changliang
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